Question

Is sin(x) even or odd ? prove with examples ?

Answer 1

sin x is an odd function.

Explanation:

f(x) = sin x

even function are those function in which when we put x = -x the function comes out to be f(-x) = f(x)

odd functions are those functions when we put x = -x then function comes out to be f(-x) = -f(x).

so,

in sin x when put x = -x

f(-x) = sin (-x)

= -sin (x)

hence, f(-x) = - f(x)

hence sin x is an odd function.

Answer 2

`\text{sin}(x)` is an odd function.

Explanation:

We are asked to prove whether
`\text{sin}(x)` is even or odd.

We know that a function
`f(x)` is even if
`f(x)=f(-x)` and a function
`f(x)` is odd, when
`f(-x)=-f(x)`.

We also know that an even function is symmetric with respect to y-axis and an odd function is symmetric about the origin.

Upon looking at our attachment, we can see that
`\text{sin}(x)` is symmetric with respect to origin, therefore,
`\text{sin}(x)` is an odd function.