Answer
1. $sin150^\circ= -\frac{1}{2}$
2. $cos150^\circ= -\frac{\sqrt 3}{2}$
3. $tan150^\circ= \frac{\sqrt 3}{3}$
4. $cot150^\circ= \sqrt 3$
5. $sec150^\circ= -\frac{2\sqrt 3}{3}$
6. $csc150^\circ= -2$
Work Step by Step
For $150^\circ$, it is in quadrant III with reference angle $\theta=180^\circ-150^\circ=30^\circ$, we have:
1. $sin150^\circ=-sin30^\circ=-\frac{1}{2}$
2. $cos150^\circ=-cos30^\circ=-\frac{\sqrt 3}{2}$
3. $tan150^\circ=tan30^\circ=\frac{\sqrt 3}{3}$
4. $cot150^\circ=cot30^\circ=\sqrt 3$
5. $sec150^\circ=-sec30^\circ=-\frac{1}{cos30^\circ}=-\frac{2\sqrt 3}{3}$
6. $csc150^\circ=-csc30^\circ=-\frac{1}{sin30^\circ}=-2$
