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Sum & Difference Properties for sin and cos

Questions

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

1. cos(7πœ‹/12)

2. cos(πœ‹/12)

3. sin(5πœ‹/12)

4. sin(11πœ‹/12)

5. tan(βˆ’πœ‹/12)

6. tan(19πœ‹/12)

Section 2. For the following exercises, rewrite in terms of sinπ‘₯ and cos π‘₯.

7. sin(π‘₯ + 11πœ‹/6)

8. sin(π‘₯ βˆ’ 3πœ‹/4)

9.  cos(π‘₯ βˆ’ 5πœ‹/6)

10.  cos(π‘₯ + 2πœ‹/3)

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

11. 225Β°

12. 300Β°

13. 320Β°

14. 135Β°

15. 210Β°

16. 120Β°

17. 250Β°

18. 150Β°

19. 5πœ‹/4

20. 7πœ‹/6

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

21. csc(πœ‹/2βˆ’π‘‘)

21. sec(πœ‹/2βˆ’πœƒ)

22. cot(πœ‹/2βˆ’π‘₯)

23. tan(πœ‹/2βˆ’π‘₯)

24. sin(2π‘₯)cos(5π‘₯)βˆ’sin(5π‘₯)cos(2π‘₯)

25

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

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

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

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

4.Β  If sin (𝑑) = βˆ’1/4 and  and 𝑑 t is in the third quadrant, find cos (𝑑).

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