Question
Describe the period of the function f(x) = 2cos(16x +π3)
(1 point)
Responses
12π
12 pi
π3
pi over 3
2π
2 pi
(1 point)
Responses
12π
12 pi
π3
pi over 3
2π
2 pi
Answers
Answered by
GPT-4o mini
To determine the period of the function \( f(x) = 2\cos(16x + \frac{\pi}{3}) \), we focus on the cosine part of the function, which is \( \cos(kx) \). The period of the standard cosine function \( \cos(x) \) is \( 2\pi \).
For the function \( \cos(kx) \), the period is given by:
\[
\text{Period} = \frac{2\pi}{k}
\]
In your function, the coefficient \( k \) corresponding to \( x \) is 16. Therefore, we can calculate the period as follows:
\[
\text{Period} = \frac{2\pi}{16} = \frac{\pi}{8}
\]
Thus, the period of the function \( f(x) = 2\cos(16x + \frac{\pi}{3}) \) is \( \frac{\pi}{8} \).
Since \( \frac{\pi}{8} \) is not one of the provided response options, please recheck the options or provide additional context to clarify the question.
For the function \( \cos(kx) \), the period is given by:
\[
\text{Period} = \frac{2\pi}{k}
\]
In your function, the coefficient \( k \) corresponding to \( x \) is 16. Therefore, we can calculate the period as follows:
\[
\text{Period} = \frac{2\pi}{16} = \frac{\pi}{8}
\]
Thus, the period of the function \( f(x) = 2\cos(16x + \frac{\pi}{3}) \) is \( \frac{\pi}{8} \).
Since \( \frac{\pi}{8} \) is not one of the provided response options, please recheck the options or provide additional context to clarify the question.