# 7.1 Trigonometric functions

You’ve probably come across the following formulae:11 1 Often remembered using the sort-of mnemonic ”SOH-CAH-TOA” (i.e. ”COS=OPPOSITE/ADJACENT, COS=ADJACENT/HYPOTENUSE, TAN=OPPOSITE/ADJACENT).

22 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

$x^{2}+y^{2}=1$

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

$\cos^{2}(\theta)+\sin^{2}(\theta)=1$

Below you can find high-precision, to-scale plots of the graphs 33 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.