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

1 Answer
Jan 2, 2017

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]}