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

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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:

$$
\frac{\pi}{2}
$$
The phase shift is $$ \frac{\pi}{2} $$.

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

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