Sketch one cycle of the graph of each cosine function. See Problem 2.

11. y = cos 2 θ y equals cosine 2 theta
12. y = − 3 cos θ y equals negative 3 cosine theta
13. y = − cos 3 t y equals negative cosine 3 t
14. y = cos π 2 θ y equals cosine , pi over 2 , theta
15. y = − cos π θ y equals negative cosine pi theta

Write a cosine function for each description. Assume that a > 0 . eh greater than 0 .  See Problem 3.

16. amplitude 2, period π
17. amplitude π 2 , pi over 2 , comma  period 3
18. amplitude π, period 2

Write an equation of a cosine function for each graph.

Solve each equation in the interval from 0 to 2π. Round your answer to the nearest hundredth. See Problem 4.

21. cos 2 t = 1 2 cosine 2 t equals , 1 half
22. 20 cos t = − 8 20 cosine t equals negative 8
23. − 2 cos π θ = 0.3 negative 2 cosine pi theta equals 0.3
24. 3 cos t 3 = 2 3 cosine , t over 3 , equals 2
25. cos 1 4 θ = 1 cosine , 1 fourth , theta equals 1
26. 8 cos π 3 t = 5 8 cosine , pi over 3 , t equals 5

B Apply

Identify the period, range, and amplitude of each function.

27. y = 3 cos θ y equals 3 cosine theta
28. y = − cos 2 t y equals negative cosine 2 t
29. y = 2 cos 1 2 t y equals 2 cosine . 1 half , t
30. y = 1 3 cos θ 2 y equals , 1 third cosine , theta over 2
31. y = 3 cos ( − θ 3 ) y equals 3 cosine . open , negative , theta over 3 , close
32. y = − 1 2 cos 3 θ y equals negative , 1 half cosine 3 theta
33. y = 16 cos 3 π 2 t y equals 16 cosine . fraction 3 pi , over 2 end fraction , t
34. y = 0 . 7 cos π t y equals 0 . 7 cosine pi t
35. Think About a Plan In Buenos Aires, Argentina, the average monthly temperature is highest in January and lowest in July, ranging from 83°F to 57°F. Write a cosine function that models the change in temperature according to the month of the year.
    • How can you find the amplitude?
    • What part of the problem describes the length of the cycle?
36. Writing Explain how you can apply what you know about solving cosine equations to solving sine equations. Use − 1 = 6 sin 2 t negative 1 equals 6 sine 2 t  as an example.

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