Question

How do you determine if `f(x)= sin x` is an even or odd function?

Answer 1

odd function

Explanation:

To determine if a function is even / odd the following applies.

• If a function is even then f(x) = (f(-x) , for all x.

Even functions have symmetry about the y-axis.

• If a function is odd then f(-x) = - f(x) , for all x.

Odd functions have symmetry about the origin.

Test for even :

f(-x) = sin(-x) = -sinx ≠ f(x) → not even

Test for odd :

`- f(x) = - sinx = f(-x) → " an odd function "`
Here is the graph. Note symmetry about O.
graph{sinx [-10, 10, -5, 5]}