QuestionFind the values of the trigonometric functions for $\theta$ where $\cot \theta=\frac{\sqrt{5}}{6}$ in quadrant III.

Studdy Solution
Since $\theta$ is in quadrant III, where sine is negative, we have$$\sin \theta = -\sqrt{\frac{36}{41}}$$So, the exact values of the remaining trigonometric functions of $\theta$ are $\tan \theta = -\frac{6}{\sqrt{5}}$, $\cos \theta = -\sqrt{\frac{5}{41}}$, and $\sin \theta = -\sqrt{\frac{36}{41}}$.