course mth 164 Complete Assignment 0: Complete the remainder of Assignment 0 as instructed under the Assts link on the homepage at 164.106.222.236. This includes the links to What to Include in Submitted Work, Precalculus II Week I and the optional DERIVE worksheet (requires approximately 2 hours for an orientation to a computer algebra and graphing system)
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13:29:24 Previous Assignments: Be sure you have completed all Preliminary Assignments as instructed on under the Assts link on the homepage at 164.106.222.236. These assignments include the q_a_orientation, and the three sets Initial Problems, Describing Graphs and Typewriter Notation from the q_a_init_pbs program. Links and explanations are included on the Assignments Page.
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RESPONSE --> ok completeed all previous assignments self critique assessment: 3
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[?w?????}??H?assignment #001 001. Radian measure and the unit circle. Precalculus II 10-19-2008
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13:54:41 Previous Assignments: Be sure you have completed all Preliminary Assignments as instructed on under the Assts link on the homepage at 164.106.222.236. These assignments include the q_a_orientation, and the three sets Initial Problems, Describing Graphs and Typewriter Notation from the q_a_init_pbs program. Links and explanations are included on the Assignments Page.
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RESPONSE --> completed all previous self critique assessment: 3
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13:56:58 `q001. Note that there are 10 activities in this assignment. Figure 37 (located under the Figures link on the Assignments page under Assignment 0) depicts a circle of radius 1 centered at the origin of a x y coordinate system. Imagine the we have 2 ants, one red and one black. Both start out moving at the same speed from the point for the positive x-axis beats the circle. The red ant crawls along the arc of the circle in the counterclockwise direction, and black ant crawls along the x-axis toward the origin. The ants proceed until the black ant reaches the origin. Both ants will have crawled the same distance, the black ant along a straight line and the red ant along an arc of the circle. At that instant the red ant will have traveled a distance equal to 1 radius of the circle, and we say that the red ant has completed 1 radian of arc. Which of the indicated points on the circle will correspond to a 1 radian arc? Note that we have indicated points a, b, c, d.
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RESPONSE --> The red ant has traveled to a point pi/4 or point d confidence assessment: 2
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13:58:09 We see visually that the point a lies at an arc distance less than the radius of the circle. We also see that the point c lies at an arc distance that is clearly greater than the radius of the circle. The only possible candidate for a 1 radian angle, which must lie at an arc distance equal to one radius, is therefore point b.
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RESPONSE --> dont see where labeled with points but realize that it would be pi/2 if angular velocity is 1 self critique assessment: 2
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13:58:48 `q002. If the first ant moves at a constant speed, moving through 1 radian every second, then approximately how long, to the nearest second, do you think it will take for the ant to move along the arc to the point where the circle meets the negative x-axis?
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RESPONSE --> 2 seconds or more confidence assessment: 1
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13:59:48 Visual examination, perhaps accompanied by a quick sketch, shows that it takes approximately 3 arcs each of one radian to get from the positive x-axis to the negative x-axis when moving along the arc of the circle. In figure 37 the points b, c and d lie at approximately 1, 2 and 3 radians. Remember that each radian corresponds to an arc distance equal to the radius of the circle. At 1 radian / second it will take about 3 seconds to move the approximately 3 radians to the negative x axis.
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RESPONSE --> yes this means that anything more than 2 seconds or past 0,-1 will move the ant to a negative self critique assessment: 3
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14:00:08 `q003. If the ant traveled at 1/2 radian per second, then after 1 second would its angular position be indicated by point a, point b, point c or point d in Figure 37?
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RESPONSE --> point b confidence assessment: 2
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14:00:17 After 1 second the angular position would be 1/2 radian, which would correspond to point a. Note that after 2 seconds the angular position would be 1 radian, corresponding to point b, and after three seconds the angular position would be 3 * 1/2 radian = 3/2 radian and the ant would be at position c.
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RESPONSE --> ok self critique assessment: 3
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14:00:46 `q004. How far will the ant travel in the process of completing 1 trip around the circle, starting and ending at the initial point where the circle meets the positive x-axis.
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RESPONSE --> approximately 2 pi or 360 deg. confidence assessment: 3
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14:00:54 The circumference of the circle is 2 pi r, where r is the radius of the circle. This is the distance traveled by the ant.
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RESPONSE --> ok self critique assessment: 3
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14:03:00 `q005. As we just saw the distance around the circle is its circumference 2 pi r, where r is the radius. Through how many radians would the ant travel from the initial point, where the circle meets the positive x-axis, if the motion was in the counterclockwise direction and ended at the original point after having completed one trip around the circle.
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RESPONSE --> 2pir confidence assessment: 3
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14:03:29 An arc displacement of r corresponds to an arc distance of 1 radian on the circle. Arc distances of 2, 3, 4, ... time the radius would correspond to 2, 3, 4, ... radians of arc. That is, arc distance of r, 2r, 3r, 4r, ... correspond to 1, 2, 3, 4, ... radians of arc. We understand by these examples that if we divide the arc distance by the radius, we will get the number of radians of angular distance. The arc distance around the circle is 2 pi r, which therefore corresponds to 2 pi r / r = 2 pi radians.
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RESPONSE --> ok self critique assessment: 3
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14:04:03 `q006. The unit circle is a circle of radius 1 centered at the origin. What are the coordinates of the points where the unit circle meets the positive x-axis, the positive y axis, the negative x-axis and the negative y axis?
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RESPONSE --> 0,1 1,0 0,-1 -1,0 confidence assessment: 3
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14:04:12 The unit circle has radius 1 and is centered at the origin, so the circle meets the positive x-axis 1 unit from the origin at (x, y) = (1,0). Similarly the circle meets the positive y-axis at the 'top' of the circle, 1 unit from the origin at (x, y) = (0,1); the circle meets the negative x-axis at (-1, 0); and the circle meets the negative y-axis at (0,-1). Figure 84 shows these points on the unit circle. Note that in this figure the small dots are located at increments of .1 unit in the x and y directions.
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RESPONSE --> ok self critique assessment: 3
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14:05:38 `q007. Without looking at Figure 84, sketch a picture of the unit circle, complete with labeled points where the circle meets the x and y axes. Indicate the arc from the standard initial point, where the circle meets the x-axis, to the point where the circle meets the positive y axis. Describe your sketch.
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RESPONSE --> the unit circle crosses all the point in a circular pattern from 0,1 to 0,1 crossing all points that are 1 radian from the origin confidence assessment: 2
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14:05:53 Your sketch should show the x and y axes and a circle of radius 1, with the points (1,0), (0, 1), (-1, 0) and (0, -1) where the circle meets the coordinate axes labeled. The arc will run along the first quadrant of the circle from (1,0) to (0,1). Your figure should match figure 84. You should be able to quickly draw this picture any time you need it.
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RESPONSE --> ok self critique assessment: 3
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14:06:40 `q008. How many radians of angular displacement correspond to the arc displacement from the standard initial point, where the circle meets the x-axis, to the point where the circle meets the positive y axis?
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RESPONSE --> pi/2 or 180 deg. confidence assessment: 3
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14:06:52 The trip around the entire circle, which corresponds to an angular displacement of 2 pi radians, corresponds to a trip from the initial point to the point where the circle meets the positive y-axis (i.e., the point (0,1)), then from this point to the point where the circle meets the negative x-axis (i.e., the point (-1,0)), then from this point to the point where the circle meets the negative y-axis (i.e., the point (0,-1)), then from this point back to the point where the circle meets the positive x-axis (i.e., the point (1,0)). Because of the symmetry of the circle, the arc corresponding to each of these displacements is the same. The arc from (1,0) to (0,1) is 1/4 of the 2 pi radian angular displacement around the entire circle, so its angular displacement is 2 pi/4 = pi/2 radians.
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RESPONSE --> ok self critique assessment: 3
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14:07:20 `q009. We have just seen that the angular position of the (1,0) point is 0 and the angular position of the (0,1) point is pi/2. What are the angular positions of the (-1,0) and (0,-1) points?
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RESPONSE --> pi, and 3pi/2 confidence assessment: 3
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14:07:42 These points are reached after successive angular displacements of pi/2. The (-1,0) point is reached from the pi/2 position by an additional angular displacement of pi/2, which puts it at angular position pi. The (0,-1) point is reached after another angular displacement of pi/2, which puts it at pi + pi/2 = 2 pi/2 + pi/2 = 3 pi/2. Note that still another angular displacement of pi/2 puts us back at the initial point, whose angular position is 0. This shows that the initial point has angular position 0, or angular position 3 pi/2 + pi/2 = 4 pi/2 = 2 pi, consistent with what we already know. You should label your picture with these angular positions pi/2, pi, 3 pi/2 and 2 pi specified at the appropriate points.
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RESPONSE --> ok self critique assessment: 3
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14:09:34 `q010. What is the angular displacement from the standard initial point of the point halfway along the arc of the circle from (1,0) to (0,1)? Note that you should begin with a sketch of the circle and of the arc specified here.
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RESPONSE --> pi/4 or 45 deg. confidence assessment: 2
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14:09:42 (1,0) is the point at which the circle meets the positive x-axis and (0,1) is the point at which the circle meets the positive y-axis. The trip along the arc of the circle from (1,0) to (0,1) will move along the first-quadrant arc from angular position 0 to angular position pi/2. Halfway along this arc, the angular position will be 1/2 * pi/2 = pi/4.
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RESPONSE --> ok self critique assessment: 3
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14:10:44 `q011. What will be the angular positions of the arc points halfway between the (0,1) and (-1,0) points of the circle? What will be the angular positions of the arc points halfway between the (-1,0) and (0,-1) points of the circle? What will be the angular positions of the arc points halfway between the (0,-1) and (1,0) points of the circle?
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RESPONSE --> pi/2 5pi/4 7pi/4 confidence assessment: 2
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14:10:55 Halfway between the (0,1) point, which corresponds to the the the position pi/2, and the (-1,0) point, which corresponds to angular position pi, will be the point lying at angular position pi/2 + pi/4 = 2 pi / 4 + pi / 4 = (2 pi + pi)/4 = 3 pi / 4. Halfway between the (-1,0) point, which corresponds to the the position pi,and the (0,-1) point, which corresponds to angular position 3 pi / 2, will be the point lying at angular position pi + pi/4 = 4 pi / 4 + pi / 4 = (4 pi + pi)/4 = 5 pi / 4. Halfway between the (0,-1) point, which corresponds to the the position 3 pi/2, and the (-1,0) point, which corresponds to angular position 2 pi, will be the point lying at angular position 3 pi/2 + pi/4 =62 pi / 4 + pi / 4 = (6 pi + pi)/4 = 7 pi / 4.
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RESPONSE --> ok self critique assessment: 3
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14:11:25 `q012. What is the angular position of the point lying 1/3 of the way along the arc of the circle between the points (1,0) and (0,1)?
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RESPONSE --> pi/3 confidence assessment: 2
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14:12:50 The arc from (1,0) to (0,1) corresponds to an angular displacement of pi/2. One-third of the arc corresponds to an angular displacement of 1/3 * pi/2 = pi/6. The angular position of the specified point is therefore pi/6.
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RESPONSE --> misiunderstood the question and used value for 2/3 of way not 1/3 self critique assessment: 3
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course mth164 query modeling exercise??????????|??x??assignment #001
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13:49:57 What is the distance between the peaks of the graph for which the angular velocity of the reference point is 3 rad / sec, and what are the maximum and minimum vertical coordinates if the circle is centered at vertical coordinate 12?
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RESPONSE --> angular velocity =3/1 12-3=9 12+3=15 =vertical coordinates confidence assessment: 1
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13:50:40 Given the values between which a cyclical quantity varies, how you determine where to position the circle that models the quantity, and how the determine the radius of the circle?
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RESPONSE --> radius = coordinate -,+ angular velocity confidence assessment: 1
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13:50:57 What is the vertical coordinate of the center of the circle, and what is the angular velocity of the reference point, for the daylight model?
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RESPONSE --> 12 confidence assessment: 2
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13:51:21 What is the vertical coordinate of the center of the circle, and what is the angular velocity of the reference point, for the temperature model?
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RESPONSE --> 3/1 is angular 12 is vertical confidence assessment: 1
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???O???????????assignment #001 001. Precalculus II 10-19-2008 ?????c???? assignment #001 001. Precalculus II 10-19-2008
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14:24:25 What is the distance between the peaks of the graph for which the angular velocity of the reference point is 3 rad / sec, and what are the maximum and minimum vertical coordinates if the circle is centered at vertical coordinate 12?
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RESPONSE --> 9 15 confidence assessment: 1
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14:28:49 Given the values between which a cyclical quantity varies, how you determine where to position the circle that models the quantity, and how the determine the radius of the circle?
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RESPONSE --> the radius is at theta and that is found by r and s and r =raduis and s =quantity confidence assessment: 1
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14:32:31 What is the vertical coordinate of the center of the circle, and what is the angular velocity of the reference point, for the daylight model?
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RESPONSE --> daylight model is derived from where vertical coordinate is found by arc distance -radius confidence assessment: 2
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14:34:06 What is the vertical coordinate of the center of the circle, and what is the angular velocity of the reference point, for the temperature model?
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RESPONSE --> angular velocity = w=domega/dtime confidence assessment: 2
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14:39:06 What is the vertical coordinate of the center of the circle, and what is the angular velocity of the reference point, for the tide model?
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RESPONSE --> angular velocity = w=domega/dtime vertical coordinate = time - referance point confidence assessment: 0
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14:41:27 What is the vertical coordinate of the center of the circle, and what is the angular velocity of the reference point, for the ocean wave model?
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RESPONSE --> vertical coordinate = most positive y coordinate angular velocity = w=domega/dtime confidence assessment: 1
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14:57:42 query ch. 5 # 78 15 in wheels at 3 rev/sec. Speed in in/s and mph: rpm?
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RESPONSE --> rpm=180 mph=16.065 in/s=94.248 confidence assessment: 2
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15:01:40 Explain your solution to this problem.
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RESPONSE --> c=2pir really this =47.124 so this means in/s =141.372 and mph =8.0325 cx3=in/s in/s/12=fpsx60=f/minx60=f/hr/5280=mph rpm=3x60 confidence assessment: 2
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15:02:04 Comm on any surprises or insights you experienced as a result of this assignment.
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RESPONSE --> need to review book more to refresh on all formulas confidence assessment: 3
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assignment #001 001. Precalculus II 10-19-2008"
course mth 164 Mr. Smith can you tell me if i am complete up to this point Complete Assignment 1:
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13:29:24 Previous Assignments: Be sure you have completed all Preliminary Assignments as instructed on under the Assts link on the homepage at 164.106.222.236. These assignments include the q_a_orientation, and the three sets Initial Problems, Describing Graphs and Typewriter Notation from the q_a_init_pbs program. Links and explanations are included on the Assignments Page.
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RESPONSE --> ok completeed all previous assignments self critique assessment: 3
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[?w?????}??H?assignment #001 001. Radian measure and the unit circle. Precalculus II 10-19-2008
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13:54:41 Previous Assignments: Be sure you have completed all Preliminary Assignments as instructed on under the Assts link on the homepage at 164.106.222.236. These assignments include the q_a_orientation, and the three sets Initial Problems, Describing Graphs and Typewriter Notation from the q_a_init_pbs program. Links and explanations are included on the Assignments Page.
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RESPONSE --> completed all previous self critique assessment: 3
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13:56:58 `q001. Note that there are 10 activities in this assignment. Figure 37 (located under the Figures link on the Assignments page under Assignment 0) depicts a circle of radius 1 centered at the origin of a x y coordinate system. Imagine the we have 2 ants, one red and one black. Both start out moving at the same speed from the point for the positive x-axis beats the circle. The red ant crawls along the arc of the circle in the counterclockwise direction, and black ant crawls along the x-axis toward the origin. The ants proceed until the black ant reaches the origin. Both ants will have crawled the same distance, the black ant along a straight line and the red ant along an arc of the circle. At that instant the red ant will have traveled a distance equal to 1 radius of the circle, and we say that the red ant has completed 1 radian of arc. Which of the indicated points on the circle will correspond to a 1 radian arc? Note that we have indicated points a, b, c, d.
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RESPONSE --> The red ant has traveled to a point pi/4 or point d confidence assessment: 2
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13:58:09 We see visually that the point a lies at an arc distance less than the radius of the circle. We also see that the point c lies at an arc distance that is clearly greater than the radius of the circle. The only possible candidate for a 1 radian angle, which must lie at an arc distance equal to one radius, is therefore point b.
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RESPONSE --> dont see where labeled with points but realize that it would be pi/2 if angular velocity is 1 self critique assessment: 2
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13:58:48 `q002. If the first ant moves at a constant speed, moving through 1 radian every second, then approximately how long, to the nearest second, do you think it will take for the ant to move along the arc to the point where the circle meets the negative x-axis?
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RESPONSE --> 2 seconds or more confidence assessment: 1
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13:59:48 Visual examination, perhaps accompanied by a quick sketch, shows that it takes approximately 3 arcs each of one radian to get from the positive x-axis to the negative x-axis when moving along the arc of the circle. In figure 37 the points b, c and d lie at approximately 1, 2 and 3 radians. Remember that each radian corresponds to an arc distance equal to the radius of the circle. At 1 radian / second it will take about 3 seconds to move the approximately 3 radians to the negative x axis.
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RESPONSE --> yes this means that anything more than 2 seconds or past 0,-1 will move the ant to a negative self critique assessment: 3
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14:00:08 `q003. If the ant traveled at 1/2 radian per second, then after 1 second would its angular position be indicated by point a, point b, point c or point d in Figure 37?
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RESPONSE --> point b confidence assessment: 2
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14:00:17 After 1 second the angular position would be 1/2 radian, which would correspond to point a. Note that after 2 seconds the angular position would be 1 radian, corresponding to point b, and after three seconds the angular position would be 3 * 1/2 radian = 3/2 radian and the ant would be at position c.
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RESPONSE --> ok self critique assessment: 3
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14:00:46 `q004. How far will the ant travel in the process of completing 1 trip around the circle, starting and ending at the initial point where the circle meets the positive x-axis.
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RESPONSE --> approximately 2 pi or 360 deg. confidence assessment: 3
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14:00:54 The circumference of the circle is 2 pi r, where r is the radius of the circle. This is the distance traveled by the ant.
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RESPONSE --> ok self critique assessment: 3
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14:03:00 `q005. As we just saw the distance around the circle is its circumference 2 pi r, where r is the radius. Through how many radians would the ant travel from the initial point, where the circle meets the positive x-axis, if the motion was in the counterclockwise direction and ended at the original point after having completed one trip around the circle.
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RESPONSE --> 2pir confidence assessment: 3
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14:03:29 An arc displacement of r corresponds to an arc distance of 1 radian on the circle. Arc distances of 2, 3, 4, ... time the radius would correspond to 2, 3, 4, ... radians of arc. That is, arc distance of r, 2r, 3r, 4r, ... correspond to 1, 2, 3, 4, ... radians of arc. We understand by these examples that if we divide the arc distance by the radius, we will get the number of radians of angular distance. The arc distance around the circle is 2 pi r, which therefore corresponds to 2 pi r / r = 2 pi radians.
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RESPONSE --> ok self critique assessment: 3
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14:04:03 `q006. The unit circle is a circle of radius 1 centered at the origin. What are the coordinates of the points where the unit circle meets the positive x-axis, the positive y axis, the negative x-axis and the negative y axis?
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RESPONSE --> 0,1 1,0 0,-1 -1,0 confidence assessment: 3
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14:04:12 The unit circle has radius 1 and is centered at the origin, so the circle meets the positive x-axis 1 unit from the origin at (x, y) = (1,0). Similarly the circle meets the positive y-axis at the 'top' of the circle, 1 unit from the origin at (x, y) = (0,1); the circle meets the negative x-axis at (-1, 0); and the circle meets the negative y-axis at (0,-1). Figure 84 shows these points on the unit circle. Note that in this figure the small dots are located at increments of .1 unit in the x and y directions.
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RESPONSE --> ok self critique assessment: 3
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14:05:38 `q007. Without looking at Figure 84, sketch a picture of the unit circle, complete with labeled points where the circle meets the x and y axes. Indicate the arc from the standard initial point, where the circle meets the x-axis, to the point where the circle meets the positive y axis. Describe your sketch.
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RESPONSE --> the unit circle crosses all the point in a circular pattern from 0,1 to 0,1 crossing all points that are 1 radian from the origin confidence assessment: 2
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14:05:53 Your sketch should show the x and y axes and a circle of radius 1, with the points (1,0), (0, 1), (-1, 0) and (0, -1) where the circle meets the coordinate axes labeled. The arc will run along the first quadrant of the circle from (1,0) to (0,1). Your figure should match figure 84. You should be able to quickly draw this picture any time you need it.
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RESPONSE --> ok self critique assessment: 3
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14:06:40 `q008. How many radians of angular displacement correspond to the arc displacement from the standard initial point, where the circle meets the x-axis, to the point where the circle meets the positive y axis?
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RESPONSE --> pi/2 or 180 deg. confidence assessment: 3
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14:06:52 The trip around the entire circle, which corresponds to an angular displacement of 2 pi radians, corresponds to a trip from the initial point to the point where the circle meets the positive y-axis (i.e., the point (0,1)), then from this point to the point where the circle meets the negative x-axis (i.e., the point (-1,0)), then from this point to the point where the circle meets the negative y-axis (i.e., the point (0,-1)), then from this point back to the point where the circle meets the positive x-axis (i.e., the point (1,0)). Because of the symmetry of the circle, the arc corresponding to each of these displacements is the same. The arc from (1,0) to (0,1) is 1/4 of the 2 pi radian angular displacement around the entire circle, so its angular displacement is 2 pi/4 = pi/2 radians.
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RESPONSE --> ok self critique assessment: 3
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14:07:20 `q009. We have just seen that the angular position of the (1,0) point is 0 and the angular position of the (0,1) point is pi/2. What are the angular positions of the (-1,0) and (0,-1) points?
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RESPONSE --> pi, and 3pi/2 confidence assessment: 3
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14:07:42 These points are reached after successive angular displacements of pi/2. The (-1,0) point is reached from the pi/2 position by an additional angular displacement of pi/2, which puts it at angular position pi. The (0,-1) point is reached after another angular displacement of pi/2, which puts it at pi + pi/2 = 2 pi/2 + pi/2 = 3 pi/2. Note that still another angular displacement of pi/2 puts us back at the initial point, whose angular position is 0. This shows that the initial point has angular position 0, or angular position 3 pi/2 + pi/2 = 4 pi/2 = 2 pi, consistent with what we already know. You should label your picture with these angular positions pi/2, pi, 3 pi/2 and 2 pi specified at the appropriate points.
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RESPONSE --> ok self critique assessment: 3
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14:09:34 `q010. What is the angular displacement from the standard initial point of the point halfway along the arc of the circle from (1,0) to (0,1)? Note that you should begin with a sketch of the circle and of the arc specified here.
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RESPONSE --> pi/4 or 45 deg. confidence assessment: 2
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14:09:42 (1,0) is the point at which the circle meets the positive x-axis and (0,1) is the point at which the circle meets the positive y-axis. The trip along the arc of the circle from (1,0) to (0,1) will move along the first-quadrant arc from angular position 0 to angular position pi/2. Halfway along this arc, the angular position will be 1/2 * pi/2 = pi/4.
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RESPONSE --> ok self critique assessment: 3
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14:10:44 `q011. What will be the angular positions of the arc points halfway between the (0,1) and (-1,0) points of the circle? What will be the angular positions of the arc points halfway between the (-1,0) and (0,-1) points of the circle? What will be the angular positions of the arc points halfway between the (0,-1) and (1,0) points of the circle?
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RESPONSE --> pi/2 5pi/4 7pi/4 confidence assessment: 2
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14:10:55 Halfway between the (0,1) point, which corresponds to the the the position pi/2, and the (-1,0) point, which corresponds to angular position pi, will be the point lying at angular position pi/2 + pi/4 = 2 pi / 4 + pi / 4 = (2 pi + pi)/4 = 3 pi / 4. Halfway between the (-1,0) point, which corresponds to the the position pi,and the (0,-1) point, which corresponds to angular position 3 pi / 2, will be the point lying at angular position pi + pi/4 = 4 pi / 4 + pi / 4 = (4 pi + pi)/4 = 5 pi / 4. Halfway between the (0,-1) point, which corresponds to the the position 3 pi/2, and the (-1,0) point, which corresponds to angular position 2 pi, will be the point lying at angular position 3 pi/2 + pi/4 =62 pi / 4 + pi / 4 = (6 pi + pi)/4 = 7 pi / 4.
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RESPONSE --> ok self critique assessment: 3
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14:11:25 `q012. What is the angular position of the point lying 1/3 of the way along the arc of the circle between the points (1,0) and (0,1)?
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RESPONSE --> pi/3 confidence assessment: 2
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14:12:50 The arc from (1,0) to (0,1) corresponds to an angular displacement of pi/2. One-third of the arc corresponds to an angular displacement of 1/3 * pi/2 = pi/6. The angular position of the specified point is therefore pi/6.
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RESPONSE --> misiunderstood the question and used value for 2/3 of way not 1/3 self critique assessment: 3
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}w?GY^?????i???g?~e???assignment #001 001. Radian measure and the unit circle. Precalculus II 10-19-2008 wr????x???????? assignment #002 002. The Fundamental Angles. Precalculus II 10-19-2008 ??????Z}???? assignment #001 001. Radian measure and the unit circle. Precalculus II 10-19-2008 ??????????H?[?assignment #002 002. The Fundamental Angles. Precalculus II 10-19-2008 j??b??W??~x?????{ assignment #002 002. The Fundamental Angles. Precalculus II 10-19-2008
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15:12:15 The reduced fractions are pi/6, pi/3, pi/2, 2 pi/3, 5 pi/6, pi, 7 pi/6, 4 pi/3, 3 pi/2, 5 pi/3, 11 pi/6 and 2 pi.
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RESPONSE --> ok self critique assessment: 3
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15:14:25 `q003. Sketch a circle centered at the origin of an x-y coordinate system, depicting the angular positions pi/6, pi/3, pi/2, 2 pi/3, 5 pi/6, pi, 7 pi/6, 4 pi/3, 3 pi/2, 5 pi/3, 11 pi/6 and 2 pi. What are the angular positions of the following points: The point 2/3 of the way along the arc between (0,1) and (-1,0) The point 1/3 of the way along the arc from (0, 1) to (-1,0) The points 1/3 and 2/3 of the way along the arc from (-1,0) to (0,-1) The points 1/3 and 2/3 of the way along the arc from (0, -1) to (0,1)??
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RESPONSE --> 5pi/6 2pi/3 confidence assessment: 3
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15:14:52 The points lying 1/3 and 2/3 of the way along the arc between the points (0,1) and (-1,0) are at angular positions 2 pi/3 and 5 pi/6; the point 2/3 of the way between these points is at angular position 5 pi/6. The points lying 1/3 and 2/3 of the way along the arc between the points (-1,0) and (0,1) are at angular positions 7 pi/6 and 4 pi/3. The points lying 1/3 and 2/3 of the way along the arc between the points (0,-1) and (1,0) are at angular positions 5 pi/3 and 11 pi/6. Note that you should be able to quickly sketch and label this circle, which depicts the angles which are multiples of pi/6, whenever you need it.
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RESPONSE --> didnt scroll down for all q's self critique assessment: 3
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15:16:47 `q004. If the red ant moves at an angular velocity of pi/4 radians every second then what will be its angular position at the end of each of the first 8 seconds?
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RESPONSE --> 2pi or 360 deg confidence assessment: 3
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15:17:08 The angular position changes by pi/4 radians every second. Starting at angular position 0, the angular positions will be pi/4, 2 pi/4, 3 pi/4, 4 pi/4, 5 pi/4, 6 pi/4, 7 pi/4, and 8 pi/4. You might have reduced these fractions the lowest terms, which is good.In any case this will be done in the next problem.
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RESPONSE --> ok self critique assessment: 3
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15:18:43 `q005. Reduce the fractions pi/4, 2 pi/4, 3 pi/4, 4 pi/4, 5 pi/4, 6 pi/4, 7 pi/4, and 8 pi/4 representing the angular positions in the last problem to lowest terms.
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RESPONSE --> pi/4 2pi/4=pi/2 3pi/4= 4pi/4=pi 5pi/4= 6pi/4=3pi/2 7pi/4= 8pi/2=2pi confidence assessment: 3
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15:18:55 The reduced fractions are pi/4, pi/2, 3 pi/4, pi, 5 pi/4, 3 pi/2, 7 pi/4, and 2 pi.
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RESPONSE --> ok self critique assessment: 3
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15:20:16 `q006. Sketch a circle centered at the origin of an x-y coordinate system, depicting the angular positions pi/4, pi/2, 3 pi/4, pi, 5 pi/4, 3 pi/2, 7 pi/4, and 2 pi. What are the angular positions of the following points: The point 1/2 of the way along the arc between (0,1) and (-1,0) The point 1/2 of the way along the arc from (0, -1) to (1,0) The point 1/2 of the way along the arc from (0,-1) to (0, -1)?
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RESPONSE --> 3pi/4 pi/4 pi/2 confidence assessment: 3
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15:20:35 The point lying 1/2 of the way along the arc between the points (0,1) and (-1,0) (the topmost and leftmost points of the circle) is at angular position 3 pi/4. The point lying 1/2 of the way along the arc between the points (0,-1) and (1,0) is at angular position 7 pi/4. The point lying 1/2 of the way along the arc between the points (-1,0) and (0,-1) is at angular position 5 pi/4. These angles are shown in Figure 21. Note that the degree equivalents of the angles are also given.
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RESPONSE --> self critique assessment:
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15:23:57 `q007. If the red ant starts at angular position pi/3 and moves at an angular velocity of pi/3 radians every second then what will be its angular position at the end of each of the first 6 seconds? Reduce your fractions to lowest terms.
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RESPONSE --> 2pi/3 pi 4pi/3 5pi/3 2pi 7pi/3 confidence assessment: 2
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15:24:05 The angular position changes by pi/3 radians every second. Starting at angular position pi/3, the angular positions after successive seconds will be 2 pi/3, 3 pi/3, 4 pi/3, 5 pi/3, 6 pi/3 and 7 pi/3, which reduce to 2 pi/3, pi, 4 pi/3, 5 pi/3, 2 pi and 7 pi/3.
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RESPONSE --> ok self critique assessment: 3
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15:24:20 `q008. Where is the angular position 7 pi/3 located?
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RESPONSE --> pi/3 or 60 deg confidence assessment: 3
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15:24:34 If you have not done so you should refer to your figure showing the positions which are multiples of pi/6. On your picture you will see that the sequence of angular positions 2 pi/3, pi, 4 pi/3, 5 pi/3, 2 pi, 7 pi/3 beginning in the first quadrant and moving through the second, third and fourth quadrants to the 2 pi position, then pi/3 beyond that to the 7 pi/3 position. The 7 pi/3 position is therefore identical to the pi/3 position.
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RESPONSE --> ok self critique assessment: 3
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15:32:35 `q009. If the red ant starts at angular position pi/3 and moves at an angular velocity of pi/4 radians every second then what will be its angular position at the end of each of the first 8 seconds? Reduce your fractions to lowest terms.
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RESPONSE --> 7pi/12 5pi/6 13pi/12 4pi/3 19pi/12 11pi/6 25pi/12 7pi/3 confidence assessment: 2
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15:34:20 The angular position changes by pi/4 radians every second. Starting at angular position pi/3, the angular positions after successive seconds will be pi/3 + pi/4, pi/3 + 2 pi/4, pi/3 + 3 pi/4, pi/3 + 4 pi/4, pi/3 + 5 pi/4, pi/3 + 6 pi/4, pi/3 + 7 pi/4 and pi/3 + 8 pi/4. These fractions must be added before being reduced to lowest terms. In each case the fractions are added by changing each to the common denominator 12. This is illustrated for pi/3 + 3 pi/4: We first multiply pi/3 by 4/4 and 3 pi/4 by 3/3, obtaining the fractions 4 pi/12 and 9 pi/12. So the sum pi/3 + 3 pi/4 becomes 4 pi/12 + 9 pi/12, which is equal to 13 pi/12. The fractions add up as follows: pi/3 + pi/4 = 7 pi/12, pi/3 + 2 pi/4 = 5 pi/6, pi/3 + 3 pi/4 = 13 pi/12, pi/3 + 4 pi/4 = 4 pi/3, pi/3 + 5 pi/4 = 19 pi/12, pi/3 + 6 pi/4 = 11 pi/6, pi/3 + 7 pi/4 = 25 pi/12 and pi/3 + 8 pi/4 = 14 pi / 3.
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RESPONSE --> ok understand formula to calculate base +distance self critique assessment: 3
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course mth 164 Complete Assignment 1:
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22:23:07 Previous Assignments: Be sure you have completed Assignment 0 as instructed under the Assts link on the homepage at 164.106.222.236 and submitted the result of the Query and q_a_ from that Assignment.
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RESPONSE --> i think that I have completed this previous assignment is this true
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22:23:27 `q001. Note that this assignment has 9 activities. If the red ant moves at an angular velocity of pi/6 radians every second, starting from the standard initial point, then what will be its angular position at the end of each of the first 12 seconds?
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RESPONSE --> 2pi confidence assessment: 2
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22:23:50 The angular position changes by pi/6 radians every second. Starting at angular position 0, the angular positions at t = 1, 2, 3, 4, ..., 12 will be pi/6, 2 pi/6, 3 pi/6, 4 pi/6, 5 pi/6, 6 pi/6, 7 pi/6, 8 pi/6, 9 pi/6, 10 pi/6, 11 pi/6, and 12 pi/6. You might have reduced these fractions the lowest terms, which is good. In any case this will be done in the next problem.
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RESPONSE --> ok only entered the last point that it was at self critique assessment: 2
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22:23:58 `q002. Reduce the fractions pi/6, 2 pi/6, 3 pi/6, 4 pi/6, 5 pi/6, 6 pi/6, 7 pi/6, 8 pi/6, 9 pi/6, 10 pi/6, 11 pi/6, and 12 pi/6 representing the angular positions in the last problem to lowest terms.
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RESPONSE --> ok confidence assessment: 3
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22:24:06 The reduced fractions are pi/6, pi/3, pi/2, 2 pi/3, 5 pi/6, pi, 7 pi/6, 4 pi/3, 3 pi/2, 5 pi/3, 11 pi/6 and 2 pi.
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RESPONSE --> ok self critique assessment: 3
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22:26:52 `q003. Sketch a circle centered at the origin of an x-y coordinate system, depicting the angular positions pi/6, pi/3, pi/2, 2 pi/3, 5 pi/6, pi, 7 pi/6, 4 pi/3, 3 pi/2, 5 pi/3, 11 pi/6 and 2 pi. What are the angular positions of the following points: The point 2/3 of the way along the arc between (0,1) and (-1,0) The point 1/3 of the way along the arc from (0, 1) to (-1,0) The points 1/3 and 2/3 of the way along the arc from (-1,0) to (0,-1) The points 1/3 and 2/3 of the way along the arc from (0, -1) to (0,1)??
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RESPONSE --> 5pi/6 4pi/6 7pi/6 9pi/6 confidence assessment: 2
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22:27:05 The points lying 1/3 and 2/3 of the way along the arc between the points (0,1) and (-1,0) are at angular positions 2 pi/3 and 5 pi/6; the point 2/3 of the way between these points is at angular position 5 pi/6. The points lying 1/3 and 2/3 of the way along the arc between the points (-1,0) and (0,1) are at angular positions 7 pi/6 and 4 pi/3. The points lying 1/3 and 2/3 of the way along the arc between the points (0,-1) and (1,0) are at angular positions 5 pi/3 and 11 pi/6. Note that you should be able to quickly sketch and label this circle, which depicts the angles which are multiples of pi/6, whenever you need it.
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RESPONSE --> ok self critique assessment: 3
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22:27:31 `q004. If the red ant moves at an angular velocity of pi/4 radians every second then what will be its angular position at the end of each of the first 8 seconds?
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RESPONSE --> 2pi confidence assessment: 2
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22:27:45 The angular position changes by pi/4 radians every second. Starting at angular position 0, the angular positions will be pi/4, 2 pi/4, 3 pi/4, 4 pi/4, 5 pi/4, 6 pi/4, 7 pi/4, and 8 pi/4. You might have reduced these fractions the lowest terms, which is good.In any case this will be done in the next problem.
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RESPONSE --> only entered the end result self critique assessment: 3
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22:28:02 `q005. Reduce the fractions pi/4, 2 pi/4, 3 pi/4, 4 pi/4, 5 pi/4, 6 pi/4, 7 pi/4, and 8 pi/4 representing the angular positions in the last problem to lowest terms.
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RESPONSE --> ok end result still 2 pi confidence assessment: 3
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22:28:08 The reduced fractions are pi/4, pi/2, 3 pi/4, pi, 5 pi/4, 3 pi/2, 7 pi/4, and 2 pi.
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RESPONSE --> ok self critique assessment: 3
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22:30:11 `q006. Sketch a circle centered at the origin of an x-y coordinate system, depicting the angular positions pi/4, pi/2, 3 pi/4, pi, 5 pi/4, 3 pi/2, 7 pi/4, and 2 pi. What are the angular positions of the following points: The point 1/2 of the way along the arc between (0,1) and (-1,0) The point 1/2 of the way along the arc from (0, -1) to (1,0) The point 1/2 of the way along the arc from (0,-1) to (0, -1)?
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RESPONSE --> 2pi/3 7pi/4 pi/2 confidence assessment: 2
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22:31:33 The point lying 1/2 of the way along the arc between the points (0,1) and (-1,0) (the topmost and leftmost points of the circle) is at angular position 3 pi/4. The point lying 1/2 of the way along the arc between the points (0,-1) and (1,0) is at angular position 7 pi/4. The point lying 1/2 of the way along the arc between the points (-1,0) and (0,-1) is at angular position 5 pi/4. These angles are shown in Figure 21. Note that the degree equivalents of the angles are also given.
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RESPONSE --> ok problem with last angle given due to coordinates are similiar and do not match answer due to coordinates given are 1/2 way between 0,-1 and 0,-1 self critique assessment: 3
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22:32:21 `q007. If the red ant starts at angular position pi/3 and moves at an angular velocity of pi/3 radians every second then what will be its angular position at the end of each of the first 6 seconds? Reduce your fractions to lowest terms.
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RESPONSE --> 2 pi end result pi/3 2pi/3 pi 4pi/3 5pi/3 confidence assessment: 3
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22:32:32 The angular position changes by pi/3 radians every second. Starting at angular position pi/3, the angular positions after successive seconds will be 2 pi/3, 3 pi/3, 4 pi/3, 5 pi/3, 6 pi/3 and 7 pi/3, which reduce to 2 pi/3, pi, 4 pi/3, 5 pi/3, 2 pi and 7 pi/3.
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RESPONSE --> self critique assessment:
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22:32:56 `q008. Where is the angular position 7 pi/3 located?
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RESPONSE --> at deg 30 confidence assessment: 3
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22:33:16 If you have not done so you should refer to your figure showing the positions which are multiples of pi/6. On your picture you will see that the sequence of angular positions 2 pi/3, pi, 4 pi/3, 5 pi/3, 2 pi, 7 pi/3 beginning in the first quadrant and moving through the second, third and fourth quadrants to the 2 pi position, then pi/3 beyond that to the 7 pi/3 position. The 7 pi/3 position is therefore identical to the pi/3 position.
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RESPONSE --> ok gave result in deg to clarify or pi/3 self critique assessment: 3
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22:38:10 `q009. If the red ant starts at angular position pi/3 and moves at an angular velocity of pi/4 radians every second then what will be its angular position at the end of each of the first 8 seconds? Reduce your fractions to lowest terms.
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RESPONSE --> end at 7pi/3 confidence assessment: 2
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22:40:50 The angular position changes by pi/4 radians every second. Starting at angular position pi/3, the angular positions after successive seconds will be pi/3 + pi/4, pi/3 + 2 pi/4, pi/3 + 3 pi/4, pi/3 + 4 pi/4, pi/3 + 5 pi/4, pi/3 + 6 pi/4, pi/3 + 7 pi/4 and pi/3 + 8 pi/4. These fractions must be added before being reduced to lowest terms. In each case the fractions are added by changing each to the common denominator 12. This is illustrated for pi/3 + 3 pi/4: We first multiply pi/3 by 4/4 and 3 pi/4 by 3/3, obtaining the fractions 4 pi/12 and 9 pi/12. So the sum pi/3 + 3 pi/4 becomes 4 pi/12 + 9 pi/12, which is equal to 13 pi/12. The fractions add up as follows: pi/3 + pi/4 = 7 pi/12, pi/3 + 2 pi/4 = 5 pi/6, pi/3 + 3 pi/4 = 13 pi/12, pi/3 + 4 pi/4 = 4 pi/3, pi/3 + 5 pi/4 = 19 pi/12, pi/3 + 6 pi/4 = 11 pi/6, pi/3 + 7 pi/4 = 25 pi/12 and pi/3 + 8 pi/4 = 14 pi / 3.
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RESPONSE --> understand formulas because pi/4+pi/2=3pi/4 self critique assessment: 2
course mth 164 FMؿƟEassignment #001
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22:51:50 query ch. 5.2 # 102 f(x) = cos(x), f(a) =1/4, find f(-a), f(a) + f(a+2`pi) + f(a - 2 `pi)
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RESPONSE --> 13.31 approximately confidence assessment: 2
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22:53:34 What is the value of f(a) + f(a+2`pi) + f(a - 2 `pi) and how did you use the even-odd and/or periodic properties of the function to obtain your result?
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RESPONSE --> I used the properties of pi to determine the solution to this function confidence assessment: 3
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22:53:41 query (no summary needed)
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RESPONSE --> ok confidence assessment: 3
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22:54:51 How does the circular model demonstrate the periodic nature of the trigonometric functions? Be specific.
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RESPONSE --> the trig funtions are proven by the repeat of solutions with regard to neg,pos. and this is the reason that the circle is used to demonstrate confidence assessment: 3
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22:55:54 How does the circular model demonstrate the even or odd nature of the sine and cosine functions? Be specific.
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RESPONSE --> this is proven by the sin and cos having the values that repeat and only differ by neg and pos values confidence assessment: 2
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22:57:09 Comm on any surprises or insights you experienced as a result of this assignment.
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RESPONSE --> yes i can and only need to know the four points at which the circle touches and the three values and the quadrants at which are pos and neg confidence assessment: 3
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~^MR~GO{ assignment #002 002. Precalculus II 10-20-2008"