This document contains examples of calculating trigonometric functions based on the position of points and angles. It discusses finding trig functions given a point (x,y), reference angles, the quadrants where trig functions are positive, and examples of calculating specific trig functions like sin, cos, and tan.

1. Find the exact values of the six trigonometricfunctions of  if the terminal side of  contains the point (8, –15). 8 -15 r (8, -15) Example 3-1a

2. 8 -15 17

3. x y r (x, y)

4. (-3, 4) Find the exact values of the six trigonometricfunctions of  if the terminal side of  contains the point (–3, 4). 5 4 -3 x = -3 y = 4 r = 5 = 5 4 3 Example 3-1b

5. Sketch 330. Then find its reference angle. 330 = 180 + 150 = 180 + 90 + 60 The reference angle is 360 –330 or 30. Example 3-3a

6. Sketch . Then find its reference angle. The reference angle is Example 3-3a

7. In which quadrants is each trig function positive? sin sin pos ALL cos tan pos (pos, pos) (neg, pos) pos (pos, neg) (neg, neg) cos tan pos pos neg pos neg r is always positive

8. Find the exact value of . 135 = 90 + 45 A S T C Example 3-4a

9. Find the exact value of . 135 = 90 + 45 pos pos Example 3-4a

10. Find the exact value of A S  = T C Example 3-4a

11. Suppose is an angle in standard position whoseterminal side is in Quadrant III and Find the exact values of the remaining five Trigonometric functions of . hyp opp -4 -3 5 Example 3-5a

12. = hyp opp -4 -3 5 Example 3-5a