NCERT · Class 11 · Mathematics · Trigonometric FunctionsIf $\cos x = -\frac{1}{2}$ and $x$ lies in the third quadrant, find the value of $\tan x$.
Step-by-Step Solution
Since $\cos x = -\frac{1}{2}$ and $x$ is in the third quadrant, $\sin x = -\sqrt{1 - \cos^2 x} = -\sqrt{1 - \left(-\frac{1}{2}\right)^2} = -\sqrt{1 - \frac{1}{4}} = -\frac{\sqrt{3}}{2}$. Therefore, $\tan x = \frac{\sin x}{\cos x} = \frac{-\frac{\sqrt{3}}{2}}{-\frac{1}{2}} = \sqrt{3}$.
Detailed Options Breakdown
Option : -\sqrt{3}
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Trigonometric Functions.
Option 1: \frac{1}{\sqrt{3}}
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Trigonometric Functions.
Option 2: \sqrt{3} (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 3: -\frac{1}{\sqrt{3}}
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Trigonometric Functions.
💡 Study Guide: This question tests core syllabus concepts from Trigonometric Functions. For formulas, key summaries, and mock exam reference guides, read the full Trigonometric Functions Revision Notes.