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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