Question
Periodic Functions Online Practice Part 2
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Question
Which of the following correctly describes the phase shift of the function f(x)=cos(3x−π2)?(1 point)
Responses
π2
Start Fraction pi over 2 End Fraction
π6
Start Fraction pi over 6 End Fraction
3π2
Start Fraction 3 pi over 2 End Fraction
−π6
negative Start Fraction pi over 6 End Fraction
Remaining Attempts : 3
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Answers
GPT-4o mini
To determine the phase shift of the function \( f(x) = \cos(3x - \frac{\pi}{2}) \), we can use the formula for the phase shift of a cosine function in the form \( f(x) = \cos(bx - c) \), which is given by:
\[
\text{Phase Shift} = \frac{c}{b}
\]
In your function, \( b = 3 \) and \( c = \frac{\pi}{2} \).
Now, substituting the values:
\[
\text{Phase Shift} = \frac{\frac{\pi}{2}}{3} = \frac{\pi}{2} \cdot \frac{1}{3} = \frac{\pi}{6}
\]
Since the traditional cosine function shifts to the right if \( c > 0 \) (in this case \(-\frac{\pi}{2}\) implies a shift to the right), we don't have to worry about a negative sign.
Thus, the phase shift of the function \( f(x) = \cos(3x - \frac{\pi}{2}) \) is:
\(\frac{\pi}{6}\)
So the correct answer is **π6** (Start Fraction pi over 6 End Fraction).
\[
\text{Phase Shift} = \frac{c}{b}
\]
In your function, \( b = 3 \) and \( c = \frac{\pi}{2} \).
Now, substituting the values:
\[
\text{Phase Shift} = \frac{\frac{\pi}{2}}{3} = \frac{\pi}{2} \cdot \frac{1}{3} = \frac{\pi}{6}
\]
Since the traditional cosine function shifts to the right if \( c > 0 \) (in this case \(-\frac{\pi}{2}\) implies a shift to the right), we don't have to worry about a negative sign.
Thus, the phase shift of the function \( f(x) = \cos(3x - \frac{\pi}{2}) \) is:
\(\frac{\pi}{6}\)
So the correct answer is **π6** (Start Fraction pi over 6 End Fraction).