If $\cos x = -\frac{1}{2}$ and $x$ lies in the third quadrant, find the value of $\tan x$.
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Question

If $\cos x = -\frac{1}{2}$ and $x$ lies in the third quadrant, find the value of $	an x$.

Accepted Answer

Since $\cos x = -\frac{1}{2}$ and $x$ is in the third quadrant, $\sin x = -\sqrt{1 - \cos^2 x} = -\sqrt{1 - \left(-\frac{1}{2}ight)^2} = -\sqrt{1 - \frac{1}{4}} = -\frac{\sqrt{3}}{2}$. Therefore, $	an x = \frac{\sin x}{\cos x} = \frac{-\frac{\sqrt{3}}{2}}{-\frac{1}{2}} = \sqrt{3}$.

Trigonometric Functions

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