Question

find the period of this function.

\\y = 2 \sin 4\theta\\

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

Explanation:

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

Step 1: Identify the period formula

For a sine function of the form \( y = a \sin(b\theta) \), the period is given by:

$$ \text{Period} = \frac{2\pi}{|b|} $$

Step 2: Calculate the period

From the given equation \( y = 2 \sin(4\theta) \), we have \( b = 4 \):

$$ \text{Period} = \frac{2\pi}{4} = \frac{1}{2}\pi $$

Answer:

$$ \frac{1}{2}\pi $$