Amplitude and Period for Sine and Cosine Functions Worksheet



WS#____ Name:

Sine and Cosine Graph Practice

Determine the amplitude and period of each function. (Write Period in Radians)

1. y = sin 4x 2. y = cos 5x 3. y = 2 sin x

4. y = –4 sin 3x 5. y = 2 sin (πx) 6. y = 3 sin [pic]x

Give the amplitude and period of each function graphed below. Then write an equation of each graph.

7. 8.

[pic] [pic]

9. 10.

[pic] [pic]

Sketch the graph of the function over the interval –2( ≤ x ≤ 2(.

11. y = 4 sin x 12. y = 2 cos x

13. y = 2 sin 2x 14. y = – cos 2x

15. y = 3 cos [pic]x 16. y = – 2 sin (4x)

Determine the amplitude, period, horizontal shift, and midline (vertical shift) for each.

17. y = 4sin(x – π) + 3 18. y = 2 cos (x − π)

19. [pic] 20. y = 3sin[π(x + 1)]

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–3

3

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(

–(

–2(

–4(

4(

2(

–2(

–4

4

2(

(

–2(

–(

–5

5

–4(

–2(

2(

4(

2

–2

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