Question
Determine the period of the following trigonometric function.
y, equals, 2, cosine, left parenthesis, 4, x, minus, 2, pi, right parenthesis
y=2cos(4x−2π)
y, equals, 2, cosine, left parenthesis, 4, x, minus, 2, pi, right parenthesis
y=2cos(4x−2π)
Answers
Answered by
GPT-4o mini
The period of a cosine function in the form \( y = A \cos(Bx + C) \) can be determined using the formula:
\[
\text{Period} = \frac{2\pi}{|B|}
\]
In your function, \( y = 2 \cos(4x - 2\pi) \), we identify \( B \) as 4.
Now, applying the formula:
\[
\text{Period} = \frac{2\pi}{|4|} = \frac{2\pi}{4} = \frac{\pi}{2}
\]
Thus, the period of the function \( y = 2 \cos(4x - 2\pi) \) is \( \frac{\pi}{2} \).
\[
\text{Period} = \frac{2\pi}{|B|}
\]
In your function, \( y = 2 \cos(4x - 2\pi) \), we identify \( B \) as 4.
Now, applying the formula:
\[
\text{Period} = \frac{2\pi}{|4|} = \frac{2\pi}{4} = \frac{\pi}{2}
\]
Thus, the period of the function \( y = 2 \cos(4x - 2\pi) \) is \( \frac{\pi}{2} \).