1. Unit 7C Review

2. 1. Identify the amplitude of the following.
𝑦=8 sin 2𝑥
𝑦=−5 cos (𝜋𝑥)
𝑦=𝑘 sec (3𝑥)
𝑦=−𝑘 csc 5𝑥

3. 1. Identify the amplitude of the following.
𝑦=8 sin 2𝑥
𝑦=−5 cos (𝜋𝑥)
𝑦=𝑘 sec (3𝑥)
𝑦=−𝑘 csc 5𝑥

4. 2. Sketch one period of 𝑦= csc 3𝑥

5. 2. Sketch one period of 𝑦= csc 3𝑥

6. 3. Simplify csc 𝑥 ⋅ tan 𝑥

7. 3. Simplify csc 𝑥 ⋅ tan 𝑥

8. 4. Identify the length of the period of …
𝑦= 3 5 sec 8𝑥
𝑦=−3 sin 3𝜋𝑥
𝑦=2 csc 𝑥 7
𝑦=− 1 2 cos 5𝑥

9. 4. Identify the length of the period of …
𝑦= 3 5 sec 8𝑥
𝑦=−3 sin 3𝜋𝑥
𝑦=2 csc 𝑥 7
𝑦=− 1 2 cos 5𝑥

10. 5. Graph 2 full periods of 𝑦=−3 sin 5𝑥

11. 5. Graph 2 full periods of 𝑦=−3 sin 5𝑥

12. 6. Prove: sec 2 𝜃 csc 2 𝜃 − sec 2 𝜃 = 𝑐𝑠 𝑐 2 𝜃

13. 6. Prove: sec 2 𝜃 csc 2 𝜃 − sec 2 𝜃 = 𝑐𝑠 𝑐 2 𝜃

14. 7. The height of a Ferris wheel is modeled by the equation ℎ= 500 cos ( π 3 𝑡) where 𝑡 is time in seconds and ℎ is the height in feet. What is the maximum height of the Ferris wheel?

15. 7. The height of a Ferris wheel is modeled by the equation ℎ= 500 cos ( π 3 𝑡) where 𝑡 is time in seconds and ℎ is the height in feet. What is the maximum height of the Ferris wheel?

16. 8. Graph 𝑦=5 cos 2𝜋 3 𝑥 , − 3 2 ≤𝑥≤ 15 4

17. 8. Graph 𝑦=5 cos 2𝜋 3 𝑥 , − 3 2 ≤𝑥≤ 15 4

18. 9. Simplify tan 𝜃 sec 𝜃

19. 9. Simplify tan 𝜃 sec 𝜃

20. 10. Using the function 𝑦=−4 sin 3𝑥
What is the minimum height of the graph?
At what x-coordinate(s) do the zeros occur in the first period.
At what x-coordinate(s) does the minimum occur in the first period.

21. 10. Using the function 𝑦=−4 sin 3𝑥
What is the minimum height of the graph?
At what x-coordinate(s) do the zeros occur in the first period.
At what x-coordinate(s) does the minimum occur in the first period.

22. 11. Graph one period of 𝑦= 1 3 sec 5 3 𝑥

23. 11. Graph one period of 𝑦= 1 3 sec 5 3 𝑥

24. 12. Prove cot 𝑥 + sec 𝑥 = cos 𝑥 + tan 𝑥 sin 𝑥

25. 12. Prove cot 𝑥 + sec 𝑥 = cos 𝑥 + tan 𝑥 sin 𝑥

26. 13. At what x-values are the asymptotes of 𝑦=−5 csc 3𝑥 in the first period.

27. 13. At what x-values are the asymptotes of 𝑦=−5 csc 3𝑥 in the first period.

28. 14. Graph 𝑦= sec 𝜋 2 𝑥 , −2≤𝑥≤3

29. 14. Graph 𝑦= sec 𝜋 2 𝑥 , −2≤𝑥≤3

30. 15. Simplify sin 2 𝜃 5−5 sin 2 𝜃

31. 15. Simplify sin 2 𝜃 5−5 sin 2 𝜃

32. 16. Give two points that the graph of 𝑦=−3 sec 2𝑥 passes through.

33. 16. Give two points that the graph of 𝑦=−3 sec 2𝑥 passes through.

34. 17. Graph one period of 𝑦= 3 5 csc 5 4 𝑥

35. 17. Graph one period of 𝑦= 3 5 csc 5 4 𝑥

36. 18. Simplify ( sec 𝜁 +1)( sec 𝜁 −1)

37. 18. Simplify ( sec 𝜁 +1)( sec 𝜁 −1)

38. 19. Give the range of y-values that are not included for the graph of 𝑦=−3 csc 5𝜋 3

39. 19. Give the range of y-values that are not included for the graph of 𝑦=−3 csc 5𝜋 3

40. 20. Prove sec 𝑥 tan 3 𝑥 + tan 𝑥 = cot 𝑥 cos 𝑥

41. 20. Prove sec 𝑥 tan 3 𝑥 + tan 𝑥 = cot 𝑥 cos 𝑥

42. 21. Simplify (1− sec 2 𝑥 )( csc 2 𝑥 −1)

43. 21. Simplify (1− sec 2 𝑥 )( csc 2 𝑥 −1)

44. 22. Simplify tan 𝑥 1+ sec 𝑥 + 1+ sec 𝑥 tan 𝑥

45. 22. Simplify tan 𝑥 1+ sec 𝑥 + 1+ sec 𝑥 tan 𝑥