# Further Maths - Odd and Even Functions

What is the definition of an even function?

\[f(x) = f(-x)\]

What is the definition of an odd function?

\[-f(x) = f(-x)\]

What is the parity of $x^2$?

Even

What is the parity of $x^3$?

Odd

What is special geometrically about even functions?

The function is symmetric with the $y$-axis.

What is special geometrically about odd functions?

The function has $180^{\circ}$ rotational symmetry with respect to the origin.

What is the parity of $\sin x$?

Odd

What is the parity of $\cos x$?

Even