Answer
$\sin \theta=-\dfrac{\sqrt {153}}{51}$
$\cos \theta=-\dfrac{4 \sqrt {153}}{51}$
$\tan \theta=\dfrac{1}{4}$
$\csc \theta=-\dfrac{\sqrt {153}}{3}$
$\sec \theta=-\dfrac{\sqrt {153}}{12}$
$\cot \theta=4$
Work Step by Step
The Trigonometric Identities can be defined as:
$\sin \theta=\dfrac{Opposite}{Hypotenuse}=-\dfrac{3}{\sqrt {153}}=-\dfrac{\sqrt {153}}{51}$
$\cos \theta=\dfrac{Adjacent}{Hypotenuse}=-\dfrac{12}{\sqrt {153}}=-\dfrac{4 \sqrt {153}}{51}$
$\tan \theta=\dfrac{Opposite}{Adjacent}=\dfrac{-3}{-12}=\dfrac{1}{4}$
$\csc \theta=\dfrac{Hypotenuse}{Opposite}=-\dfrac{\sqrt {153}}{3}$
$\sec \theta=\dfrac{Hypotenuse}{Adjacent}=\dfrac{-5}{4 \sqrt{153}}=-\dfrac{\sqrt {153}}{12}$
$\cot \theta=\dfrac{Adjacent}{Opposite}=\dfrac{-12}{-3}=4$
