What is the equation of sinusoidal function with the amplitude 3 and period pi/4?

May 1, 2018

$y = 3 \sin \left(8 x\right)$

Explanation:

The parent function is $\sin x$ so this is where we start.

$y = \sin x$

The amplitude of this sine wave is 1. To make the amplitude 3, we multiply the sine by 3.

$y = 3 \sin x$

The period of this sine wave is 2$\pi$. We want the period to be $2 \frac{\pi}{8}$ so we need to multiply $x$ by 8.

$y = 3 \sin \left(8 x\right)$

This satisfies the requirements of the problem statement.

graph{3sin(8x) [-1, 1, -5, 5]}