1. Find the values of the six trigonometric functions for the angle θ. Assume a = 7, b = 24, c = 25.

2. Find the values of the six trigonometric functions for the angle θ. Assume a = 1, c = 4.

3. Find the values of the six trigonometric functions for the angle θ.

4. Find the values of the six trigonometric functions for the angle θ.

5. Find the exact values of x and y. Assume  s =  4.

6. Find the exact values of x and y. Assume a =  9.

7. Find the exact values of x and y. Assume  s =  8.

8. Find the exact values of the trigonometric functions for the acute angle θ. sin θ= 4/5

9. Find the exact values of the trigonometric functions for the acute angle θ. cos θ = 12/13.

10. Find the exact values of the trigonometric functions for the acute angle θ. tan θ =3/4.

11. Find the exact values of the trigonometric functions for the acute angle θ. cot θ = 24/7.

12. Find the exact values of the trigonometric functions for the acute angle θ. sec θ =8/7.

13. A forester, 150 feet from the base  of a redwood tree, observes that the angle between the  ground and the top of the tree is 55°. Estimate the height of the tree. (Round your answer to one decimal place.)

14. Use the Pythagorean identities to write the expression as an integer.

(a) tan²  9β  - sec² 9β

(b)  9 tan²  β  - 9 sec² β

15. Use the Pythagorean identities to write the expression as an  integer.

(a) csc² 6α  - cot² 6α

(b) 6 csc² α  - 6 cot² α

16. Use the Pythagorean identities to write the expression as an  integer.

(a) 8 sin² θ  + 8 cos² θ

(b) 8 sin²(θ/4) + 8 cos² (θ/4) 

17. Use fundamental identities to write the first expression in terms of the second, for any acute angle θ. cos θ, cot θ

18. Find the exact values of the six trigonometric functions of θ if θ is in standard position and the terminal side of θ  is in the specified quadrant and satisfies the given   condition.

III;  parallel to the line  2y - 9x + 7 =  0

19. Find the exact values of the six trigonometric functions of θ  if θ  is in standard position and the terminal side of θ  is in the given quadrant and satisfies the given condition.

II; Parallel to the line through A(-1, 10) and B(-2,   13)

20. Find the exact values of the six trigonometric functions of each angle, whenever possible. (If there is no solution, enter NO  SOLUTION.)

(a) 900°

(b) -810°

(c) 10π

(d) 9π/2

21. Find the quadrant containing θ  if the given conditions are true.

quadrant I
quadrant II
quadrant III
quadrant IV

(a) cos θ < 0 and sin θ > 0
(b) sin θ < 0 and cot θ < 0
(c) csc θ < 0 and sec θ < 0
(d) sec θ < 0 and tan θ < 0

22. Find the quadrant containing θ if the given conditions are true.

Quadrant I
Quadrant II
Quadrant III
Quadrant IV

(a) tan θ < 0 and cos θ > 0
(b) sec θ < 0 and tan θ < 0
(c) csc θ < 0 and cot θ < 0
(d) cos θ < 0 and csc θ < 0

23. Use fundamental identities to find the values of the trigonometric functions for the given conditions.

tan θ = -3/4 and sin θ > 0

24. Use fundamental identities to find the values of the trigonometric functions for the given conditions.

cot θ = 4/3 and cos θ < 0

25. Use fundamental identities to find the values of the trigonometric functions for the given conditions.

sin θ = -4/5 and sec θ > 0

26. Use fundamental identities to find the values of the trigonometric functions for the given conditions.

cos θ = 1/2 and sin θ < 0.