CBSE · Class 11 · Mathematics · Trigonometric FunctionsWhat is the value of $\tan\left(\frac{19\pi}{3}\right)$?
Step-by-Step Solution
We can write $\frac{19\pi}{3} = 6\pi + \frac{\pi}{3} = 3(2\pi) + \frac{\pi}{3}$. Since $\tan(2n\pi + x) = \tan x$, we have $\tan\left(6\pi + \frac{\pi}{3}\right) = \tan\left(\frac{\pi}{3}\right) = \sqrt{3}$.
Detailed Options Breakdown
Option : \frac{1}{\sqrt{3}}
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Trigonometric Functions.
Option 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: -1
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.