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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. 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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  2. 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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  3. 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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