course Mth 164 FN}assignment #002
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00:16:16 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: 0
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Ӄ{Hq߅ӝ assignment #002 002. The Fundamental Angles. Precalculus II 09-11-2008
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00:44:56 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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hCFn볚rԖ assignment #002 002. The Fundamental Angles. Precalculus II 09-11-2008
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00:59:48 `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 --> 0 or 2pi. That would be 12pi/6 radians. confidence assessment: 2
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01:00:34 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 --> Didnt realized I needed to name all of the second positions. self critique assessment: 3
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01:06:08 `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 --> pi/6=pi/6. 2pi/6=pi/3. 3 pi/6=pi/2. 4pi/6=2pi/3. 5pi/6=5pi/6. 6pi/6=pi. 7pi/6=7pi/6. 8pi/6=4pi/3. 9pi/6=3pi/2. 10pi/6=5pi/3. 11pi/6=11pi/6. 12pi/6=2pi confidence assessment: 3
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01:06:19 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 --> self critique assessment: 3
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01:10:27 `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. 7pi/6. 4pi/3. 5pi/3. 11pi/6 confidence assessment: 3
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01:10:35 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 --> self critique assessment: 3
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01:12:54 `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 0, it would be a full circle 8*pi/4=8pi/4=2pi confidence assessment: 3
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01:13:41 09-11-2008 01:13:41 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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NOTES -------> Didnt know you wanted all positions, but I do know them
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01:14:52 `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, pi/2, 3pi/4, pi. 5pi/4, 3pi/2, 7pi/4, 2pi confidence assessment: 2
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01:15:04 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 --> self critique assessment: 3
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01:17:09 `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 --> 3 pi/4. 7 pi/4. There is no arc it is the same position, 3pi/2 confidence assessment: 3
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01:18:33 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 --> You have a typo on the last part of the question self critique assessment: 2
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01:21:03 `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 --> pi/3, 2pi/3, pi, 4pi/3, 5pi/3, 2pi, pi/3 confidence assessment: 3
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01:21:39 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: 3
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01:22:20 `q008. Where is the angular position 7 pi/3 located?
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RESPONSE --> pi/3 confidence assessment: 3
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01:22:33 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 --> self critique assessment: 3
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01:28:43 `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 --> confidence assessment:
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01:32:02 `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, 5 pi/6, 13 pi/12, 4 pi/3, 19 pi/12, 11 pi/6, 25 pi/12, 7 pi/3. confidence assessment: 3
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01:34:52 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 --> That last one should be 7 pi/3. 25pi/12+3pi/12=28pi/12=7pi/3 self critique assessment: 2
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