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