Answer
$\sin \theta =$ $\frac{a}{c}$ ; $\cos \theta =$ $\frac{b}{c}$ ; $\tan \theta =$ $\frac{a}{b}$ ; $\csc \theta =$ $\frac{c}{a}$ ; $\sec \theta =$ $\frac{c}{b}$ ; $\cot \theta =$ $\frac{b}{a}$
Work Step by Step
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:
$\begin{align}
& \sin \theta =\frac{\text{opposite side}}{\text{hypotenuse}} \\
& =\frac{a}{c}
\end{align}$
$\begin{align}
& \cos \theta =\frac{\text{adjacent side}}{\text{hypotenuse}} \\
& =\frac{b}{c}
\end{align}$
$\begin{align}
& \tan \theta =\frac{\text{opposite side}}{\text{adjacent side}} \\
& =\frac{a}{b}
\end{align}$
$\begin{align}
& \csc \theta =\frac{\text{hypotenuse}}{\text{opposite side}} \\
& =\frac{c}{a}
\end{align}$
$\begin{align}
& \sec \theta =\frac{\text{hypotenuse}}{\text{adjacent side}} \\
& =\frac{c}{b}
\end{align}$
$\begin{align}
& \cot \theta =\frac{\text{adjacent side}}{\text{opposite side}} \\
& =\frac{b}{a}
\end{align}$
