co urse Mth 164 assignment #001001. Radian measure and the unit circle.
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20:57:23 Goals for this Assignment include but are not limited to the following: 1. Construct a unit circle showing all standard angular positions which are multiples of pi/6 or pi/4. 2. Given starting point and angular velocity model motion on the unit circle. 3. Relate angular displacement on the unit circle to arc distance and vice versa. Click once more on Next Question/Answer for a note on Previous Assignments.
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RESPONSE --> self critique assessment:
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??????X????? assignment #002 002. The Fundamental Angles. Precalculus II 07-01-2008 ??I?????{?n???j?? assignment #002 002. The Fundamental Angles. Precalculus II 07-01-2008
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20:59:17 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 --> self critique assessment:
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21:08:04 `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 --> It chages by pi/6 every second. It goes pi/6, 2ppi/6, 3pi/6, 4pi/6, 5pi/6, 6pi/6, 7pi/6, 8pi/6, 9pi/6, 10pi/6, 11pi/6, and 12pi/6. confidence assessment: 2
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21:09:53 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 --> I see how this is done and I understand how you find the answer. Sometimes it is easier to reduce the fraction to understand it better. self critique assessment: 3
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21:11:48 `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 --> You would get pi/6, pi/3, pi/2, 2pi/3, 5pi/6, pi, 7pi/6, 4pi/3, 3pi/2, 5pi/3, 11pi/6 and 2 pi confidence assessment: 2
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21:12:40 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 --> I get this. If the numbers are divisable by each other you reduce them. If it is an odd number it says the same. self critique assessment: 3
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21:15:16 `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 --> They are 1/3 and 2/3 alog the arc. The anular positions are at 2pi/3 and 5pi/6. Then you have 7pi/6 and 4pi/3. Thn there is 5pi/3 and 11pi/6. confidence assessment: 2
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21:20:08 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 --> I see that I left out the points. The arc points are (0,1) and (-1,0) and thi is at 2pi/3 and 5pi/6. The arc points (0,-1) and (1,0) is at 7pi/6 and 4pi/3.. The arc points at (0,-1) and (1,0) are 5pi/3 and 11pi/6. self critique assessment: 3
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21:21:40 `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 --> It changes by pi/4. THe positios will be pi/4, 2pi/4, 3pi/4, 4pi/4, 5pi/4, 6pi/4, 7pi/4, and 8pi/4 since it is at 8 seconds. confidence assessment: 2
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21:24:08 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 --> I understand how this is done. Since it is for 8 seconds you start at 1 and thn proceed to take pi/4 startig at 1 and ending at 8. self critique assessment: 3
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21:25:51 `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 --> You get pi/4, pi/2, 3pi/4, pi, 5pi/4, 3pi/2, 7pi/4 and 2pi. confidence assessment: 2
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21:27:04 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 --> The orginial fractions get reduced if it is possible. The even numbers are easier to reduce and the odd numbers usually stay the same. self critique assessment: 3
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21:30:10 `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 --> Since it is 1/2 around it, at the arc the points are (0,1) and (-1,0) and is positioned t 3pi/4. The next one is at 7pi/4 and then you have 5pi/4. confidence assessment: 2
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21:36:05 `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 --> I see how this is done and I understand it. confidence assessment: 3
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21:39:19 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 --> I seem to have skipped something here. I see how this is done though. When you have pi/3 you get 2pi/3, 3pi/3, 4pi/3, 5pi/3, 6pi/3 and 7pi/3. When you reduce it I see how you go about it. You would have 2pi/3, pi, 4pi/3, 5pi/3, 2pi and 7pi/3. self critique assessment: 3
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21:41:14 `q008. Where is the angular position 7 pi/3 located?
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RESPONSE --> You get 2pi/3, 3pi/3, 4pi/3, 5pi/3, 6pi/3 and 7pi/3. confidence assessment: 2
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21:42:13 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 --> I see how it moves from the first quadrant and then moves to the second, third and fourth to get to 2pi. self critique assessment: 3
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21:45:14 `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 --> You would have pi/3 + pi/4, pi/3 + 2pi/4, pi/3 + 3pi/4, pi/3 + 4pi/4, pi/3+ 5pi/4, pi/3 + 6pi/4, pi/3 + 7pi/4 and pi/3 + 8pi/4. confidence assessment: 2
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21:50:30 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 --> I see that you have toadd these together so thst they can be reduced. You will also have to chnge the commin denominator which wuld be 12. You then have pi/3 + pi/4 = 7pi/12, pi/3+2pi/4=5pi/6, pi/3+3pi/4= 13pi/12, pi/3+ 4pi/4= 4pi/3, pi/3 + 5pi/4= 19pi/12, pi/3+6pi/4=11pi/6, pi/3+7pi/4= 25pi/12 and pi/3+8pi/4=14pi/3. self critique assessment: 3
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21:50:49 Complete Assignment 1: Includes Class Notes #'s 1-2 (Class Notes are accessed under the Lectures button at the top of the page and are included on the CDs starting with CD #1). Introductory Experience: Pendulum modeled by Motion on a Circle (as instructed on Assts page) Sketching Exercise Graphing Vertical Position; Effects of Angular Velocity, Radius, Starting Point (as instructed on Assts page) Modeling Exercise: Circular Models (click on link on Assts page) Text Section 5.1, 'Blue' Problems (i.e., problems whose numbers are highlighted in blue) and odd multiples of 3 in text and the Web version of Ch 5 Problems Section 5.1 (use the link in the Assts page to access the problems). When you have completed the entire assignment run the Query program. Submit SEND files from Query and q_a_.
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RESPONSE --> Completed self critique assessment: 3
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