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

Jan 2, 2017

Period is damped with respect to |x|. The ampliture is $\sqrt{5}$.
The phase is $- {\tan}^{- 1} \left(2\right)$

#### Explanation:

This is a period-damped oscillation.

The damping ( $\downarrow$) 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 $\sqrt{5}$.

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