### Home > PC > Chapter 8 > Lesson 8.2.1 > Problem8-78

8-78.

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

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.

Sketch a diagram and label.

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