It has an amplitude of 3 and a period of 4pi/5 Find the equation of this wave as a sine function.

y = 3 sin 2.5 x

Step-by-step explanation:

Given that a sine function has an amplitude of 3 and a period of 4pi/5

There is no phase shift or vertical shift. Hence y would be y only and x is x only.

Consider original sine function y = sinx

This has period 2pi and amplitude = 1

Since new amplitude is 3, we must have coefficient of sinx as 3

i. e. y = 3 sinx makes the amplitude 3.

To change period from 2pi to 4pi/5, we change the coefficient of x from 1 to

5/2

i. e. y = 3 sin 2.5 x is the equation of this function.