\begin{aligned} &\text { (c) (5 points) Given that } \alpha \text { is an acute angle in standard position, and } P=\left(\frac{\sqrt{3}}{3}, \frac{\sqrt{6}}{3}\right) \text { is on the terminal }\\

&\text { side of } \alpha, \text { find } \cos (\pi-\alpha) \end{aligned} \begin{aligned} &\text { (a) (5 points) Given that } \alpha \text { is an acute angle, find an expression for } \cot \left(\frac{\pi}{2}-\alpha\right) \text { in terms of } \sin (\alpha) \text { and }\\ &\cos (\alpha) \text { only. } \end{aligned} \text { b) }(5 \text { points }) \text { Given that } \csc (\theta)=8 \text { and } \theta \text { is on the second quadrant, find } \tan (\theta) \text { . } 5. (20 points) In each of the cases below, use the given information to find the required trigonometric function value. Briefly show or explain which identities or properties of angles, trigonometric functions,or of the unit circle you are using.