Answer
$\displaystyle \sin\theta=\frac{\sqrt{2}}{2}$
$\displaystyle \cos\theta=\frac{\sqrt{2}}{2}$
$\tan\theta=1$
$\cot\theta=1$
$\sec\theta=\sqrt{2}$
$\csc\theta=\sqrt{2}$
Work Step by Step
For any real number $s$ represented by a directed arc on the unit circle,
$\sin s=y\quad \cos s=x \quad \displaystyle \tan s=\frac{y}{x} (x\neq 0)$
$\displaystyle \csc s=\frac{1}{y} (y\neq 0)\quad \displaystyle \sec s=\frac{1}{x} (x\neq 0) \displaystyle \quad\cot s=\frac{x}{y} (y\neq 0)$.
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$\displaystyle \sin\theta=y=\frac{\sqrt{2}}{2}$
$\displaystyle \cos\theta=x=\frac{\sqrt{2}}{2}$
$\displaystyle \tan\theta=\frac{y}{x}=\frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}}=1$
$\displaystyle \cot\theta=\frac{x}{y}=\frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}}=1$
$\displaystyle \sec\theta=\frac{1}{x}=\frac{1}{\frac{\sqrt{2}}{2}}=\frac{2}{\sqrt{2}}=\frac{2}{\sqrt{2}}\cdot\frac{\sqrt{2}}{\sqrt{2}}=\sqrt{2}$
$\displaystyle \csc\theta=\frac{1}{y}=\frac{1}{\frac{\sqrt{2}}{2}}=\frac{2}{\sqrt{2}}=\frac{2}{\sqrt{2}}\cdot\frac{\sqrt{2}}{\sqrt{2}}=\sqrt{2}$