Question

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

Answer 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)

Answer 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. <b>y = 2 sin 4(x - π/8) + 1</b> 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)

Answer 3

first answer line should be

1. <b>y = 2 sin 4(x - π/8) + 1</b> or y = 2 sin (4x - π/2) + 1