Question

find the period of this function.
y = 2 sin 4θ
?/?π

Explanation:

Step1: Recall the period formula for sine function

The general form of a sine function is \( y = A\sin(B\theta + C)+D \), and the period \( P \) is given by \( P=\frac{2\pi}{|B|} \).

Step2: Identify the value of \( B \) in the given function

In the function \( y = 2\sin(4\theta) \), we have \( B = 4 \).

Step3: Calculate the period

Using the period formula \( P=\frac{2\pi}{|B|} \), substitute \( B = 4 \) into the formula. So \( P=\frac{2\pi}{4}=\frac{\pi}{2} \). To match the form \( \frac{?}{?}\pi \), the numerator is \( 1 \) and the denominator is \( 2 \).

Answer:

The period of the function \( y = 2\sin(4\theta) \) is \( \frac{1}{2}\pi \), so the numerator is \( 1 \) and the denominator is \( 2 \).