Question

What is the phase shift of the following equation:
Y= 3cos(1/3(x - π/2))

Answer 1

The phase shift of the equation Y=3cos(1/3(x-π/2)) is 3π/2 radians or 270 degrees, which represents a rightward shift of the cosine graph.

Step-by-step explanation:

The phase shift of the equation Y = 3cos(1/3(x - π/2)) can be determined by examining the argument of the cosine function. The general form of the cosine function with a phase shift is Y = A cos(B(x - C)), where C/B is the phase shift. In the given equation, B is 1/3 and C is π/2, so the phase shift is π/2 divided by 1/3, which simplifies to 3π/2 radians or 270 degrees. This indicates that the graph of the cosine function is shifted to the right by 3π/2 radians.