Answer
1. $sin\theta=\frac{2\sqrt {2}}{3}$
2. $tan\theta=-2\sqrt {2}$
3. $cot\theta= -\frac{\sqrt {2}}{4}$
4. $sec\theta= -3$
5. $csc\theta= \frac{3\sqrt {2}}{4}$
Work Step by Step
Given $cos\theta=-\frac{1}{3}$ and $\theta$ in quadrant II, we have $x=-1, r=3, y=\sqrt {3^2-(-1)^2}=2\sqrt {2}$, thus
1. $sin\theta=\frac{2\sqrt {2}}{3}$
2. $tan\theta=-2\sqrt {2}$
3. $cot\theta=\frac{1}{tan\theta}=-\frac{\sqrt {2}}{4}$
4. $sec\theta=\frac{1}{cos\theta}=-3$
5. $csc\theta=\frac{1}{sin\theta}=\frac{3\sqrt {2}}{4}$
