Question

What is a periodic function? Find the period of sin²x+cos³x​

Answer 1

a function returning to the same value at regular intervals.

Y=sin⁴x + cos⁴ x

Therefore ,

let, f(x)=sin⁴x +cos⁴x

Period of sin⁴x will be π [power is even]

Period of cos⁴x will be π [power is even]

So, LCM rule will say period is π but

f(π /2+x)=(sin(π/2+x))⁴ +(cos(π/2+x)

=cos⁴x+sin⁴x

=f(x)

So, period is (π/2)

Answer 2

A function returning to the same value at regular intervals