Answer
$\sin \theta = \frac{\sqrt7}{4}$
$\cos \theta = \frac{3}{4}$
$\csc \theta = \frac{4\sqrt7}{7}$
$\cot \theta = \frac{3\sqrt7}{7}$
Work Step by Step
We have the following information :
$\tan \theta = \frac{y}{x} = \frac{\sqrt7}{3}$
$\sec \theta = \frac{r}{x} = \frac{4}{3}$
It's clear, that :
$x=3$
$y=\sqrt7$
$r=4$
So, the remaining $4$ trigonometric functions will be :
$\sin \theta = \frac{y}{r} = \frac{\sqrt7}{4}$
$\cos \theta = \frac{x}{r} = \frac{3}{4}$
$\csc \theta = \frac{r}{y} = \frac{4}{\sqrt7}= \frac{4\sqrt7}{7}$
$\cot \theta = \frac{x}{y} = -\frac{3}{\sqrt7} = \frac{3\sqrt7}{7}$
