Question
What is the phase shift of the function f(x)=sin(x−π2) ?(1 point) Responses 1 1 π4 Start Fraction pi over 4 End Fraction π pi π2
Answers
GPT-4o mini
To find the phase shift of the function \( f(x) = \sin(x - \frac{\pi}{2}) \), we can use the standard form of the sine function, which is:
\[
f(x) = a \sin(b(x - c)) + d
\]
In this case, we can rewrite the function as:
\[
f(x) = \sin\left(1\cdot\left(x - \frac{\pi}{2}\right)\right)
\]
From this, we can identify that \( c = \frac{\pi}{2} \). The phase shift \( c \) indicates how much the function has been shifted horizontally to the right. Since the phase shift is given as \( c \) in the form \( x - c \), a positive \( c \) means a shift to the right.
Thus, the phase shift of the function \( f(x) = \sin(x - \frac{\pi}{2}) \) is:
\[
\frac{\pi}{2}
\]
Therefore, the correct answer is \( \frac{\pi}{2} \).
\[
f(x) = a \sin(b(x - c)) + d
\]
In this case, we can rewrite the function as:
\[
f(x) = \sin\left(1\cdot\left(x - \frac{\pi}{2}\right)\right)
\]
From this, we can identify that \( c = \frac{\pi}{2} \). The phase shift \( c \) indicates how much the function has been shifted horizontally to the right. Since the phase shift is given as \( c \) in the form \( x - c \), a positive \( c \) means a shift to the right.
Thus, the phase shift of the function \( f(x) = \sin(x - \frac{\pi}{2}) \) is:
\[
\frac{\pi}{2}
\]
Therefore, the correct answer is \( \frac{\pi}{2} \).