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)]
-----------------------
–3
3
2(ᱎ᱖᱘ᱜᱞᱠᲢᲶᴒᴔᴖᴢᵈᵊᵐᵚᵤᵴᵶᵸᵼᶊᶌᶲᶴ쳙쳂첵첫첫钡ꮉ觌翌ꇌ畿枉剿̩뭪පĈ栖挄Z䩃䩏䩑ࡕ嘁Ĉ䩞䩡̛jᘀ屨屉伀J儀J唀Ĉ䩞ᘒ䕨啰伀J儀J帀Jᘒ屨屉伀J儀J帀Jᘕ屨屉㔀脈䩏䩑䩞ᔘ屨屉ᘀ꽨п伀J儀J帀Jᘒ䐐伀J儀J帀Jᘒ꽨п伀J儀J帀Jᔘ摨㵶ᘀ扨Ḫ伀J儀J帀Jᘒᝨ썚伀J儀J帀Jᔘ屨屉ᘀ䐐伀J儀J帀Jᔘ屨屉ᘀꡨ伀J儀J帀Jᔘ屨屉ᘀ써伀J儀J帀Jᔘ屨屉ᘀ
(
–(
–2(
–4(
4(
2(
–2(
–4
4
2(
(
–2(
–(
–5
5
–4(
–2(
2(
4(
2
–2
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