QPaperGen

\[ \text{Given:}\quad
\cos x = -\frac{1}{2}, \quad x \text{ lies in the third quadrant}
\]

Using the Pythagorean identity:
\[
\sin^2 x = 1 - \cos^2 x = 1 - \left(-\frac{1}{2}\right)^2 = \frac{3}{4}
\]
\[
\sin x = -\frac{\sqrt{3}}{2}
\]
(in third quadrant, sine is negative)
\[\]

Other functions:
\[
\tan x = \frac{\sin x}{\cos x} = \sqrt{3}
\]
\[
\csc x = \frac{1}{\sin x} = -\frac{2}{\sqrt{3}}
\]
\[
\sec x = \frac{1}{\cos x} = -2
\]
\[
\cot x = \frac{\cos x}{\sin x} = \frac{1}{\sqrt{3}}
\]