The sinusoid y=3cos(x+3)-2 has which of the following?
a. phase shift of 3 to the right
b. phase shift of 3 to the left
c. vertical shift up of 2
d. horizontal stretch by factor of 3
you mean compared to y = 3cos x ??
then it would be b)
To determine the phase shift, vertical shift, and horizontal stretch of the sinusoid, we can analyze the given equation y=3cos(x+3)-2.
The general form of a sinusoidal function is y = A*cos(Bx-C)+D, where:
A represents the amplitude,
B represents the horizontal stretch or compression,
C represents the phase shift, and
D represents the vertical shift.
By comparing the given equation with the general form, we can identify the characteristics mentioned in the options:
a. Phase shift of 3 to the right:
The phase shift in the general form is given by C. In the given equation, the phase shift is -3 (opposite sign due to the equation x+3), which implies a phase shift of 3 to the LEFT. Therefore, option a is incorrect.
b. Phase shift of 3 to the left:
As explained above, the phase shift in the given equation is -3, resulting in a phase shift of 3 to the left. Therefore, option b is correct.
c. Vertical shift up of 2:
The vertical shift in the general form is given by D. In the given equation, the vertical shift is -2, which implies a vertical shift DOWN by 2. Therefore, option c is incorrect.
d. Horizontal stretch by a factor of 3:
The horizontal stretch/compression in the general form is given by 2π/B. In the given equation, B is 1, so the horizontal stretch factor is 2π/1 = 2π. There is no horizontal stretch by a factor of 3. Therefore, option d is incorrect.
Therefore, the correct answer is:
b. Phase shift of 3 to the left.