## Precalculus (6th Edition) Blitzer

$\sin \theta =$ $\frac{a}{c}$ ; $\cos \theta =$ $\frac{b}{c}$ ; $\tan \theta =$ $\frac{a}{b}$ ; $\csc \theta =$ $\frac{c}{a}$ ; $\sec \theta =$ $\frac{c}{b}$ ; $\cot \theta =$ $\frac{b}{a}$
Here, $a$ is length of side opposite $\theta$, $b$ is length of side adjacent to $\theta ,$ and $c$ is the length of the hypotenuse. Thus: \begin{align} & \sin \theta =\frac{\text{opposite side}}{\text{hypotenuse}} \\ & =\frac{a}{c} \end{align} \begin{align} & \cos \theta =\frac{\text{adjacent side}}{\text{hypotenuse}} \\ & =\frac{b}{c} \end{align} \begin{align} & \tan \theta =\frac{\text{opposite side}}{\text{adjacent side}} \\ & =\frac{a}{b} \end{align} \begin{align} & \csc \theta =\frac{\text{hypotenuse}}{\text{opposite side}} \\ & =\frac{c}{a} \end{align} \begin{align} & \sec \theta =\frac{\text{hypotenuse}}{\text{adjacent side}} \\ & =\frac{c}{b} \end{align} \begin{align} & \cot \theta =\frac{\text{adjacent side}}{\text{opposite side}} \\ & =\frac{b}{a} \end{align}