Answer
$sin~θ=\frac{\sqrt 2}{2}$
$cos~θ=\frac{\sqrt 2}{2}$
$tan~θ=1$
$csc~θ=\sqrt 2$
$sec~θ=\sqrt 2$
$cot~θ=1$
Work Step by Step
First, let's evaluate the hypotenuse:
$(hyp)^2=(opp)^2+(adj)^2$
$hyp=\sqrt {4^2+4^2}=\sqrt {16\times2}=4\sqrt 2$
$sin~θ=\frac{opp}{hyp}=\frac{4}{4\sqrt 2}=\frac{1}{\sqrt 2}\frac{\sqrt 2}{\sqrt 2}=\frac{\sqrt 2}{2}$
$cos~θ=\frac{adj}{hyp}=\frac{4}{4\sqrt 2}=\frac{1}{\sqrt 2}\frac{\sqrt 2}{\sqrt 2}=\frac{\sqrt 2}{2}$
$tan~θ=\frac{opp}{adj}=\frac{4}{4}=1$
$csc~θ=\frac{hyp}{opp}=\frac{4\sqrt 2}{4}=\sqrt 2$
$sec~θ=\frac{hyp}{adj}=\frac{4\sqrt 2}{4}=\sqrt 2$
$cot~θ=\frac{adj}{opp}=\frac{4}{4}=1$
