Question

How do you know if `y=sin^2(x)` is an even or odd function?

Answer 1

`y = sin^2 x " is an even function"`

Explanation:

`color(brown)("What is an even function?")`
1. `color(green)("An even function is symmetric about the y-axis."`
2. `color(purple)(f(-x) = f(x)`

`color(orange)("What is an odd function?"`
1. `color(blue)("An odd function is symmetric about the origin".`
2. `color(red)(f(-x) = -f(x)`

Given : `y = sin^2x`

`f(x) = sin^2 x`

`f(-x) = sin^2 (-x) = (sin(-x))^2 = (-sin x)^2 = sin^2 x = f(x)`

Hence it is an even function.

graph{(sin x)^2 [-10.54, 9.46, -5.32, 4.68]}