Amplitude and Period for Sine and Cosine Functions Worksheet



Name _______________ Algebra 2 – More Practice with Sine and Cosine Graphs

Period _________

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

Amplitude _________ Amplitude _________ Amplitude _________

Period ____________ Period ____________ Period ____________

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

Amplitude _________ Amplitude _________ Amplitude _________

Period ____________ Period ____________ Period ____________

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

7. 8.

[pic] [pic]

Amplitude _______ Period ____________ Amplitude _______ Period ____________

Sine Equation _______________________ Sine Equation _______________________

Cosine Equation _____________________ Cosine Equation _____________________

9. 10.

[pic] [pic]

Amplitude _______ Period ____________ Amplitude _______ Period ____________

Sine Equation _______________________ Sine Equation _______________________

Cosine Equation _____________________ Cosine Equation _____________________

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

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

[pic] [pic]

13. y = 2 sin 2x 14. y = – cos 2x

[pic] [pic]

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

[pic] [pic]

Determine the amplitude, period, phase shift, and vertical shift for each.

17. [pic] 18. y = 2 cos (x − π)

Amplitude _______________ Amplitude _______________

Period ___________________ Period ___________________

Phase Shift _______________ Phase Shift _______________

Vertical Shift _____________ Vertical Shift _____________

19. [pic] 20. [pic]

Amplitude _______________ Amplitude _______________

Period ___________________ Period ___________________

Phase Shift _______________ Phase Shift _______________

Vertical Shift _____________ Vertical Shift _____________

Identify the equation of the graphs below for each Sine and Cosine.

21. 22.

[pic] [pic]

Sine Equation _________________________ Sine Equation _______________________

Cosine Equation ________________________ Cosine Equation ______________________

-----------------------

–3

3

2(

(

–(

–2(

–4(

4(

2(

–2(

–4

4

2(

(

–2(

–(

–5

5

–4(

–2(

2(

4(

2

–2

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