December 12, 2012
Section 4.4 Graphs of Sine and Cosine:
Sinusoids
•t
P(t) = (x, y) = (cos t, sin t)
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(-1, 0)
(0, 1)
t
r=1
(1, 0)
0
(0, -1)
The graph of (t, sin t)
Domain: (−∞, ∞)
Range: [−1, 1]
Period: 2π
[-2π, 2π] [-4, 4]
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December 12, 2012
Graph y = cos x and y = sin x in the same
zoom trig window.
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y = sin x
y = cos x
1
−2π
−π
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−1
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•π
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2π
Now graph y = 2 sin x
Graph two periods of y = sin 3x.
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1
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−1
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December 12, 2012
A function is a sinusoid if it can be written
in the form f(x) = a sin (bx + c) + d where
a, b, c, and d are constants and neither a
nor b is 0.
|a| is the amplitude of the sinusoid.
is the period of the sinusoid.
Graphically, the period is the length of
one full cycle of the wave.
is the frequency of the sinusoid.
Graphically, the frequency is the number
of complete cycles the wave completes in
a unit interval.
f(x) = 4 sin (3x + π) − 1
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Amplitude:
Period:
Frequency:
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12-12-12
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