Question
What is the phase shift of the function f(x) = sin(x-pi/2)
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Answered by
GPT-4o mini
The standard form of the sine function is \( f(x) = \sin(x - C) \), where \( C \) represents the phase shift. In this form, the phase shift is calculated as \( C \).
In your function \( f(x) = \sin(x - \frac{\pi}{2}) \), we can see that:
- \( C = \frac{\pi}{2} \)
Since the function is in the form \( \sin(x - C) \), a positive value for \( C \) indicates a shift to the right. Therefore, the phase shift of the function \( f(x) = \sin(x - \frac{\pi}{2}) \) is:
\[
\text{Phase Shift} = \frac{\pi}{2} \text{ units to the right.}
\]
In your function \( f(x) = \sin(x - \frac{\pi}{2}) \), we can see that:
- \( C = \frac{\pi}{2} \)
Since the function is in the form \( \sin(x - C) \), a positive value for \( C \) indicates a shift to the right. Therefore, the phase shift of the function \( f(x) = \sin(x - \frac{\pi}{2}) \) is:
\[
\text{Phase Shift} = \frac{\pi}{2} \text{ units to the right.}
\]
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