Question

What is the phase shift of the function f(x)=\sin \left(x-(\pi)/(2)\right)?
A. (\pi)/(2)
B. (\pi)/(4)
C. 1
D. \pi

Answer 1

To determine the phase shift of the function \( f(x) = \sin\left(x - \frac{\pi}{2}\right) \), we can use the standard form of the sine function, which is given by:

\[
f(x) = \sin(k(x - d))
\]

where \( d \) is the phase shift.

In this case, we can rewrite the function:

\[
f(x) = \sin\left(1 \cdot \left(x - \frac{\pi}{2}\right)\right)
\]

Here, \( k = 1 \) and \( d = \frac{\pi}{2} \). The phase shift is positive when you shift to the right and negative when you shift to the left. The formula for the phase shift in this context is \( d \).

Thus, the phase shift is:

\[
\text{Phase shift} = \frac{\pi}{2}
\]

Given the options:

A. \( \frac{\pi}{2} \)
B. \( \frac{\pi}{4} \)
C. 1
D. \( \pi \)

The correct answer is:

**A. \( \frac{\pi}{2} \)**

Answer 2

Are you sure

Answer 3

Yes, the phase shift calculation is correct.

For the function \( f(x) = \sin\left(x - \frac{\pi}{2}\right) \), the phase shift can be determined from the expression inside the sine function. In the general sine function form \( f(x) = \sin(k(x - d)) \), the term \( d \) represents the phase shift.

In this case:

- The function can be expressed as \( f(x) = \sin\left(1 \cdot \left(x - \frac{\pi}{2}\right)\right) \).
- Here, we have \( d = \frac{\pi}{2} \).

Since \( d \) is subtracted from \( x \), it indicates a shift to the right by \( \frac{\pi}{2} \).

So, the phase shift is indeed \( \frac{\pi}{2} \) to the right.

The answer remains:

**A. \( \frac{\pi}{2} \)**.