What is the phase shift of the function \( f(x)=\sin \left(x-\frac{\pi}{2}\right) ? \) (1 point) \( \frac{\pi}{\frac{\pi}{2}} \) \( \frac{\pi}{4} \) 1

To find the phase shift of the function \( f(x) = \sin\left(x - \frac{\pi}{2}\right) \), we can use the general form of the sine function, which is given by: \[ f(x) = \sin(kx - c) \] In this case, we can rewrite the function as: \[ f(x) = \sin\left(1 \cdot x - \frac{\pi}{2}\right) \] Here, \( k = 1 \) and \( c = \frac{\pi}{2} \). The phase shift is calculated using the formula: \[ \text{Phase Shift} = \frac{c}{k} \] Substituting the values we have: \[ \text{Phase Shift} = \frac{\frac{\pi}{2}}{1} = \frac{\pi}{2} \] Since the function is of the form \( \sin(x - c) \), the phase shift is to the right by \( \frac{\pi}{2} \). Thus, the phase shift of the function \( f(x) = \sin\left(x - \frac{\pi}{2}\right) \) is \( \frac{\pi}{2} \). None of the provided options match this result, but the correct answer is: \[ \frac{\pi}{2} \]