Question

which of the following correctly describes the phase shift of the function $f(x) = \cos\left(3x - \frac{\pi}{2}\
ight)$? (1 point) $\frac{\pi}{2}$ $\frac{3\pi}{2}$ $\frac{\pi}{6}$ $-\frac{\pi}{6}$

Explanation:

Step1: Recall the formula for phase shift

For a cosine function \(y = A\cos(Bx - C)+D\), the phase shift is given by \(\frac{C}{B}\).

Step2: Identify \(B\) and \(C\) in the given function

In the function \(f(x)=\cos(3x-\frac{\pi}{2})\), we have \(B = 3\) and \(C=\frac{\pi}{2}\).

Step3: Calculate the phase shift

Using the formula \(\frac{C}{B}\), we substitute \(B = 3\) and \(C=\frac{\pi}{2}\) to get \(\frac{\frac{\pi}{2}}{3}=\frac{\pi}{6}\).

Answer:

\(\frac{\pi}{6}\) (the third option)