Question
What is the period of the function f(t) = cos (5t + pi / 2) - 3?
(1 point)
2/5
3/5
2pi/5
pi
2pi
(1 point)
2/5
3/5
2pi/5
pi
2pi
Answers
GPT-4o mini
The period of the function \( f(t) = \cos(5t + \frac{\pi}{2}) - 3 \) is determined by the cosine term.
The standard cosine function \( \cos(x) \) has a period of \( 2\pi \). When the argument of the cosine function is of the form \( kt \), where \( k \) is a constant, the period is given by:
\[
\text{Period} = \frac{2\pi}{|k|}
\]
In this case, the argument of the cosine function is \( 5t + \frac{\pi}{2} \). The coefficient \( k \) is 5, so the period of the function is:
\[
\text{Period} = \frac{2\pi}{|5|} = \frac{2\pi}{5}
\]
Thus, the period of the function \( f(t) = \cos(5t + \frac{\pi}{2}) - 3 \) is \( \frac{2\pi}{5} \).
The correct answer is **\( \frac{2\pi}{5} \)**.
The standard cosine function \( \cos(x) \) has a period of \( 2\pi \). When the argument of the cosine function is of the form \( kt \), where \( k \) is a constant, the period is given by:
\[
\text{Period} = \frac{2\pi}{|k|}
\]
In this case, the argument of the cosine function is \( 5t + \frac{\pi}{2} \). The coefficient \( k \) is 5, so the period of the function is:
\[
\text{Period} = \frac{2\pi}{|5|} = \frac{2\pi}{5}
\]
Thus, the period of the function \( f(t) = \cos(5t + \frac{\pi}{2}) - 3 \) is \( \frac{2\pi}{5} \).
The correct answer is **\( \frac{2\pi}{5} \)**.