Unit 7C Review

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

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

2. Sketch one period of 𝑦= csc 3𝑥

2. Sketch one period of 𝑦= csc 3𝑥

3. Simplify csc 𝑥 ⋅ tan 𝑥

3. Simplify csc 𝑥 ⋅ tan 𝑥

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

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

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

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

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

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

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?

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?

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

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

9. Simplify tan 𝜃 sec 𝜃

9. Simplify tan 𝜃 sec 𝜃

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.

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.

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

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

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

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

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

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

14. Graph 𝑦= sec 𝜋 2 𝑥 , −2≤𝑥≤3

14. Graph 𝑦= sec 𝜋 2 𝑥 , −2≤𝑥≤3

15. Simplify sin 2 𝜃 5−5 sin 2 𝜃

15. Simplify sin 2 𝜃 5−5 sin 2 𝜃

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

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

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

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

18. Simplify ( sec 𝜁 +1)( sec 𝜁 −1)

18. Simplify ( sec 𝜁 +1)( sec 𝜁 −1)

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

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

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

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

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

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

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

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