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
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)
first answer line should be
1. y = 2 sin 4(x - π/8) + 1 or y = 2 sin (4x - π/2) + 1
To write the equation of a sine wave, we can use the general form:
y = A*sin(B(x - C)) + D
where:
- A is the amplitude of the wave,
- B is the reciprocal of the period of the wave,
- C is the phase shift,
- D is the vertical shift.
Let's find the equations for each given scenario:
1.
Amplitude = 2
Period = π/2
Phase shift = π/8
Vertical shift = 1
In this case, A = 2, B = 1/(π/2) = 2/π, C = π/8, and D = 1.
Therefore, the equation of the sine wave is:
y = 2*sin((2/π)(x - π/8)) + 1
2.
Amplitude = 4
Period = 3
Phase shift = 2
Vertical shift = -1
Here, A = 4, B = 1/3, C = 2, and D = -1.
So the equation becomes:
y = 4*sin((1/3)(x - 2)) - 1
3.
Amplitude = 4
Period = π
Phase shift = -(π/3)
Vertical shift = 0
In this case, A = 4, B = 1/π, C = -(π/3), and D = 0.
Hence, the equation of the sine wave is:
y = 4*sin((1/π)(x + π/3)) + 0
Note: The vertical shift (D) is always added at the end but with no calculation since it only moves the graph up or down.
1. y = 2(sin(4x - pi/8)) + 1
2. y = 4(sin((2pi/3)x - 2)) - 1
3. y = 4(sin(2x + pi/3)