Answer
$\sin \theta =\dfrac{y}{r}=\dfrac{5\sqrt {29}}{29} \\ \cos \theta =\dfrac{x}{r}=\dfrac{-2\sqrt {29}}{29} \\ \tan \theta =\dfrac{y}{x}=\dfrac{-5}{2}$
and
$\csc \theta =\dfrac{r}{y}=\dfrac{\sqrt {29}}{5} \\ \sec \theta =\dfrac{r}{x}=\dfrac{-\sqrt {29}}{2} \\ \cot \theta =\dfrac{x}{y}=\dfrac{-2}{5}$
Work Step by Step
Here, $ x=-2; y=5$ $ r=\sqrt {(-2)^2+(5)^2}=\sqrt {29}$
The trigonometric ratios are as follows:
$\sin \theta =\dfrac{y}{r}=\dfrac{5\sqrt {29}}{29} \\ \cos \theta =\dfrac{x}{r}=\dfrac{-2\sqrt {29}}{29} \\ \tan \theta =\dfrac{y}{x}=\dfrac{-5}{2}$
and
$\csc \theta =\dfrac{r}{y}=\dfrac{\sqrt {29}}{5} \\ \sec \theta =\dfrac{r}{x}=\dfrac{-\sqrt {29}}{2} \\ \cot \theta =\dfrac{x}{y}=\dfrac{-2}{5}$
