Sum & Difference Properties for sin and cos

Questions

Section 1. For the following exercises, find the exact value.

1. cos(7𝜋/12)

2. cos(𝜋/12)

3. sin(5𝜋/12)

4. sin(11𝜋/12)

5. tan(−𝜋/12)

6. tan(19𝜋/12)

Section 2. For the following exercises, rewrite in terms of sin𝑥 and cos 𝑥.

7. sin(𝑥 + 11𝜋/6)

8. sin(𝑥 − 3𝜋/4)

9.  cos(𝑥 − 5𝜋/6)

10.  cos(𝑥 + 2𝜋/3)

Section 3. Use the unit circle and/or the properties for finding sin and cos values to solve these questions:

11. 225°

12. 300°

13. 320°

14. 135°

15. 210°

16. 120°

17. 250°

18. 150°

19. 5𝜋/4

20. 7𝜋/6

Section 4. For the following exercises, simplify the given expression.

21. csc(𝜋/2−𝑡)

21. sec(𝜋/2−𝜃)

22. cot(𝜋/2−𝑥)

23. tan(𝜋/2−𝑥)

24. sin(2𝑥)cos(5𝑥)−sin(5𝑥)cos(2𝑥)

25. 

Review: Section 5. For the following exercises, find the requested value.

1.  If cos (𝑡)= 1/7 and 𝑡 t is in the fourth quadrant, find sin (𝑡).

2. If cos (𝑡)= 2/9 and 𝑡 t is in the first quadrant, find sin (𝑡).

3.  If sin (𝑡) = 3/8 and 𝑡 t is in the second quadrant, find cos (𝑡).

4.  If sin (𝑡) = −1/4 and  and 𝑡 t is in the third quadrant, find cos (𝑡).