# Further Maths - Odd and Even Functions

> Source: https://ollybritton.com/notes/a-level/further-maths/topics/odd-and-even-functions/ · Updated: 2020-11-11 · Tags: school, further-maths, a-level

##### 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

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