Answer
$-\frac{\sqrt 2}{2}$, $\frac{\sqrt 2}{2}$, $ -1$, $ -1$, $ \sqrt 2$, and $ -\sqrt 2$.
Work Step by Step
Given $\theta=315^\circ$ (quadrant IV), we have $sin\theta =-sin45^\circ=-\frac{\sqrt 2}{2}$, $cos\theta =cos45^\circ=\frac{\sqrt 2}{2}$, $tan\theta =-tan45^\circ=-1$, $cot\theta = \frac{1}{tan\theta}=-1$, $sec\theta = \frac{1}{cos\theta}=\sqrt 2$, and $csc\theta = \frac{1}{sin\theta}=-\sqrt 2$.
