CPM Homework Help : PC Problem 8-78

Find the exact value of $\cot θ$ given $\cos θ = \frac { \sqrt { 3 } } { 2 }$ and $\csc θ \lt 0$ .

Hint 1:

Since the $\csc\left(θ\right) \lt 0$ , it must be in Quadrants III or IV.
Since the $\cos\left(θ\right) \gt 0$ , it must be in Quadrant IV.

Hint 2:

Sketch a diagram and label.

Diagram:

Hint:

$\text{cot}(\theta)=\frac{\text{adjacent side}}{\text{opposite side}}$