Answer
See graph and explanations.
Work Step by Step
1. Plot the point $(2,-7)$ (red) as shown in the figure.
2. Connect the point with the origin, the positive angle formed with the x-axis is $\theta$
3. We have $sin\theta=\frac{-7}{\sqrt {2^2+7^2}}=-\frac{7}{\sqrt {53}}=-\frac{7\sqrt {53}}{53}$
4. We have $cos\theta=\frac{2}{\sqrt {2^2+7^2}}=\frac{2}{\sqrt {53}}=\frac{2\sqrt {53}}{53}$
5. We have $tan\theta=-\frac{7}{2}$
6. We have $cot\theta=-\frac{2}{7}$
7. We have $sec\theta=\frac{1}{cos\theta}=\frac{\sqrt {53}}{2}$
8. We have $csc\theta=\frac{1}{sin\theta}=-\frac{\sqrt {53}}{7}$
