# How do you use use quotient identities to explain why the tangent and cotangent function have positive values for angles in the third quadrant?

Nov 5, 2014

If the terminal side of an angle $\theta$ is in the third quadrant, then

$\pi < \theta < \frac{3 \pi}{2}$,

which makes both $\sin \theta$ and $\cos \theta$ negative.

Since negative divided by negative is positive, both

$\tan \theta = \frac{\sin \theta}{\cos \theta}$ and $\cot \theta = \frac{\cos \theta}{\sin \theta}$

are positive.

I hope that this was helpful.