4.4--Graphs of Sine and Cosine: Sinusoids
y = a sin (bx + c) + d
or
y = a cos (bx + c) + d
amplitude = a
normal period of sin & cos = 2π
period =
2π
b
horizontal shift = -
c
b
vertical shift = d
1) Compare the graphs of the following sinusoidal functions:
y = sin x
y = 2 sin x
y = 5 sin x
y = -5 sin x
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4.4--Graphs of Sine and Cosine: Sinusoids
2) Compare the graphs of the following sinusoidal functions:
y = sin x
y = sin 2x
y = sin 8x
y = sin ½x
Period and frequency are reciprocals.
period =
2π
b
frequency =
b
2π
2
4.4--Graphs of Sine and Cosine: Sinusoids
Find the amplitude, period, and frequency for each graph:
AMP
3)
y = 4 sin (3x) + 9
4)
y = 8 cos (x - 4)
5)
y = -7 sin (x/2)
6)
y =
1
2
PER
FREQ
cos (2x - 5)
7) Compare the graphs of the following sinusoidal functions:
y = sin x
y = sin (x - π/4)
y = sin (x + π)
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4.4--Graphs of Sine and Cosine: Sinusoids
8) Compare the graphs of the following sinusoidal functions:
y = sin x
y = sin x + 3
y = sin x - 5
9) What happens to y = sin x when it's shifted π/2 to the left?
It becomes y = cos x.
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4.4--Graphs of Sine and Cosine: Sinusoids
Construct a sinusoid that has the given amplitude and period
that goes through the given point:
10)
amplitude = 4, period = π, passing through (0, 1):
11)
amplitude = 2.7, period = π/9, passing through (2, 0):
Find the amplitude, period, horizontal shift, and vertical
shift for each graph:
AMP
12)
y = - sin (5x) - 2
13)
y = -6 cos (8x - 4 )
14)
y = sin (4x - 5) + 3
15)
y = cos (.5x + 2) + 1
PER
HORIZ
VERT
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