# 7.1 Trigonometric functions

You’ve probably come across the following formulae:^{1}^{1}
1
Often remembered
using the sort-of mnemonic ”SOH-CAH-TOA” (i.e. ”COS=OPPOSITE/ADJACENT,
COS=ADJACENT/HYPOTENUSE, TAN=OPPOSITE/ADJACENT).

^{2}

^{2}2 The Greek letter $\theta$ is often used for angles in the same way as the variable $x$ is used to denote unknowns.

$\displaystyle\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}$ | (7.1) | ||

$\displaystyle\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}$ | (7.2) | ||

$\displaystyle\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$ | (7.3) |

The way we work out the actual values of $\cos(\theta)$, $\sin(\theta)$ and $\tan(\theta)$ is by making things as easy as possible for ourselves; we draw a triangle inside a circle with radius one. From here, we know that

$\displaystyle\sin(\theta)=\frac{y}{1}$ | ||

$\displaystyle\cos(\theta)=\frac{x}{1}$ |

Note that because this is the unit circle, we have

And if we substitute $\cos(\theta)$ and $\sin(\theta)$ we get that

Below you can find high-precision,
to-scale plots of the graphs ^{3}^{3}
3
Protip: learn how
to draw the graphs without having to thtink about it! of both $\sin(x)$ and
$\cos(x)$ as well as a diagram of the unit circle.