Question

How do you find the amplitude, period, phase shift given `y=2sin(x^2)+cos(x^2)`?

Answer 1

Period is damped with respect to |x|. The ampliture is `sqrt5`.
The phase is `-tan^(-1)(2)`

Explanation:

This is a period-damped oscillation.

The damping ( `darr`) is with respect to |x|.

The two terms can be combined to form.

`sqrt 5 sin (x^2+tan^(-1)2))`.

So, phase is `-tan^(-1)2` and theamplitude iis `sqrt5`.

graph{(y-2sin(x^2)-cos(x^2))(y-2.236)(y+2.235)=0 [-10, 10, -5, 5]}