January 07, 2011
Section 4.4 Graphs of Sine and Cosine:
Sinusoids
•t
P(t) = (x, y) = (cos t, sin t)
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t
r=1
0
The graph of (t, sin t)
Domain: (−∞, ∞)
Range: [−1, 1]
Period: 2π
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Graph y = 2 sin x
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−2π
1
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−π
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−1
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π
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2π
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Graph y = sin 3x
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1
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−1
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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
Amplitude:
Period:
Frequency:
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Graph y = cos x and y = sin x in the same
zoom trig window.
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