Answer:
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.
