Practice and Problem-Solving Exercises

A Practice

Use the graph below to find the value of y = sin θ y equals sine theta  for each value of θ. See Problem 1.

6. π 2  radians pi over 2 . radians
7. 3 radians
8. 4 radians
9. 5 radians
10. 3 π 2  radians fraction 3 pi , over 2 end fraction . radians
11. 7 π 4  radians fraction 7 pi , over 4 end fraction . radians

Determine the number of cycles each sine function has in the interval from 0 to 2π. Find the amplitude and period of each function. See Problems 2 and 3.

Sketch one cycle of each sine curve. Assume a > 0 . eh greater than 0 .  Write an equation for each graph. See Problem 4.

15. amplitude 2, period 2 π 3 fraction 2 pi , over 3 end fraction
16. amplitude 1 3 , 1 third , comma  period π
17. amplitude 4, period 4π
18. amplitude 3, period 2π
19. amplitude 1, period 2
20. amplitude 1.5, period 3

Sketch one cycle of the graph of each sine function. See Problem 5.

21. y = sin π θ y equals sine pi theta
22. y = sin 3 θ y equals sine 3 theta
23. y = − sin π 2 θ y equals negative sine , pi over 2 , theta
24. y = 2 sin π θ y equals 2 sine pi theta
25. y = 4 y equals 4  sin 1 2 1 half θ
26. y = − 4 y equals negative 4  sin 1 2 1 half θ

Find the period of each sine curve. Then write an equation for each sine function. See Problem 6.

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