Question

question
determine the period of the following trigonometric function.

$y = - 8\sin(2x)$

Explanation:

Step1: Recall the formula for the period of a sine function

The general form of a sine function is \(y = A\sin(Bx + C)+D\), and its period is \(T=\frac{2\pi}{|B|}\).

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

For the function \(y=-8\sin(2x)\), we have \(B = 2\).

Step3: Calculate the period

Substitute \(B = 2\) into the period formula \(T=\frac{2\pi}{|B|}\). So \(T=\frac{2\pi}{|2|}=\pi\).

Answer:

\(\pi\)