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 side opposite to $θ$:
$(hyp)^2=(opp)^2+(adj)^2$
$(7\sqrt 2)^2=(opp)^2+7^2$
$49(2)-49=(opp)^2$
$49=(opp)^2$
$opp=7$
$sin~θ=\frac{opp}{hyp}=\frac{7}{7\sqrt 2}=\frac{1}{\sqrt 2}\frac{\sqrt 2}{\sqrt 2}=\frac{\sqrt 2}{2}$
$cos~θ=\frac{adj}{hyp}=\frac{7}{7\sqrt 2}=\frac{1}{\sqrt 2}\frac{\sqrt 2}{\sqrt 2}=\frac{\sqrt 2}{2}$
$tan~θ=\frac{opp}{adj}=\frac{7}{7}=1$
$csc~θ=\frac{hyp}{opp}=\frac{7\sqrt 2}{7}=\sqrt 2$
$sec~θ=\frac{hyp}{adj}=\frac{7\sqrt 2}{7}=\sqrt 2$
$cot~θ=\frac{adj}{opp}=\frac{7}{7}=1$
