Answer
1. $sin135^\circ= \frac{\sqrt 2}{2}$
2. $cos135^\circ= -\frac{\sqrt 2}{2}$
3. $tan135^\circ= -1$
4. $cot135^\circ= -1$
5. $sec135^\circ= -\sqrt 2$
6. $csc135^\circ =\sqrt 2$
Work Step by Step
For $135^\circ$, it is in quadrant II with reference angle $\theta=180^\circ-135^\circ=45^\circ$, we have:
1. $sin135^\circ=sin45^\circ=\frac{\sqrt 2}{2}$
2. $cos135^\circ=-cos45^\circ=-\frac{\sqrt 2}{2}$
3. $tan135^\circ=-tan45^\circ=-1$
4. $cot135^\circ=-cot45^\circ=-1$
5. $sec135^\circ=-sec45^\circ=-\frac{1}{cos45^\circ}=-\sqrt 2$
6. $csc135^\circ=csc45^\circ=\frac{1}{sin45^\circ}=\sqrt 2$
