Write the equation of a sine wave (also called sine curve) given:
1.
amplitude = 2
period = pi/2
phase shift = pi/8
vertical shift = 1
2.
amplitude = 4
period = 3
phase shift = 2
vertical shift = 1
3.
amplitude = 4
period = pi
phase shift = (pi/3)
vertical shift = 0
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3 answers

1. y = 2(sin(4x  pi/8)) + 1
2. y = 4(sin((2pi/3)x  2))  1
3. y = 4(sin(2x + pi/3) 👍
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answered by eric 
I disagree with your phase shift
in general:
y = a sin k(x  d) + c
the phase shift is d. Notice that the period indicator k is factored out
In your answer we have ... sin(4x  π/8) ...
or ... sin 4(x  π/32)...
So the phase shift of your equation would be π/32
correct answers:
1. y = 2 sin 4(x  π/8) + 1 or y = 2 sin (4x 
2. y = 4 sin (2π/3)(x  2))  1 or y = 4 sin (2π/3)x  4π/3)  1
3. y = 4 sin 2(x + π/3) 👍
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answered by Reiny 
first answer line should be
1. y = 2 sin 4(x  π/8) + 1 or y = 2 sin (4x  π/2) + 1 👍
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answered by Reiny
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