Answer
$\sin \theta=\dfrac{2 \sqrt 5}{5}$
$\cos \theta=\dfrac{\sqrt 5}{5}$
$\tan \theta=\dfrac{8}{4}=2$
$\csc \theta=\dfrac{\sqrt 5}{2}$
$\sec \theta=\dfrac{4 \sqrt {5}}{4}=\sqrt 5$
$\cot \theta=\dfrac{1}{2}$
Work Step by Step
The Trigonometric Identities can be defined as:
$\sin \theta=\dfrac{Opposite}{Hypotenuse}=\dfrac{8}{4 \sqrt {5}}=\dfrac{2 \sqrt 5}{5}$
$\cos \theta=\dfrac{Adjacent}{Hypotenuse}=\dfrac{4}{4 \sqrt {5}}=\dfrac{\sqrt 5}{5}$
$\tan \theta=\dfrac{Opposite}{Adjacent}=\dfrac{8}{4}=2$
$\csc \theta=\dfrac{Hypotenuse}{Opposite}=\dfrac{4 \sqrt {5}}{8}=\dfrac{\sqrt 5}{2}$
$\sec \theta=\dfrac{Hypotenuse}{Adjacent}=\dfrac{4 \sqrt {5}}{4}=\sqrt 5$
$\cot \theta=\dfrac{Adjacent}{Opposite}=\dfrac{4}{8}=\dfrac{1}{2}$
