Introduction to the Unit Circle

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Show your work for each problem.

1.
What is the radius of the unit circle?
1. a)2
2. b)0
3. c)1
4. d)
2.
What are the coordinates of the center of the unit circle?
1. a)
2. b)
3. c)
4. d)
3.
What is ?
4.
What is ?
5.
On the unit circle, what does the x-coordinate of a point represent?
1. a)
2. b)
3. c)The radius
4. d)
6.
What is ?
7.
What is ?
8.
In which quadrant are both sine and cosine positive?
1. a)Quadrant III
2. b)Quadrant II
3. c)Quadrant IV
4. d)Quadrant I
9.
Find using the unit circle.
10.
Find the coordinates of the point on the unit circle at .
11.
In which quadrant is positive and negative?
1. a)Quadrant II
2. b)Quadrant III
3. c)Quadrant IV
4. d)Quadrant I
12.
What is ?
13.
Find using reference angles.
14.
If a point on the unit circle has coordinates , verify it lies on the unit circle.
15.
What is true about for any angle ?
1. a)It always equals 2
2. b)It depends on the angle
3. c)It always equals 0
4. d)It always equals 1