Question

what is the period of the following function?

\\y = \cos 5\theta\\

\\\frac{?}{}\pi\\

Explanation:

⚡ Using what you learned: Amplitude, Period, Phase Shift

Step 1: Identify the coefficient of the angle

For a cosine function of the form \( y = \cos(B\theta) \), identify the value of \( B \):

$$ B = 5 $$

Step 2: Calculate the period

The formula for the period \( P \) of a cosine function is:

$$ P = \frac{2\pi}{|B|} $$

Substitute \( B = 5 \) into the formula:

$$ P = \frac{2}{5}\pi $$

Answer:

$$ \frac{2}{5}\pi $$