Question

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

Answer 1

Answer:

sin x is an odd function.

Step-by-step 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

Answer:

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

Step-by-step 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.