Find the principal value of $tan^{- 1} (- 3)$ .

easy MCQ 2 marks Class 12 · Mathematics · Inverse Trigonometric Functions

$- \frac{π}{3}$
$\frac{2 π}{3}$
$\frac{π}{3}$
$- \frac{2 π}{3}$

Answer

- \frac{π}{3}

The correct answer is $- \frac{π}{3}$ — Since $tan (- \frac{π}{3}) = - 3$ and $- \frac{π}{3} \in (- \frac{π}{2}, \frac{π}{2})$ , the required principal value is $- \frac{π}{3}$ .

Step-by-step solution

Recall that the principal value of $tan^{- 1} y$ lies in $(- \frac{π}{2}, \frac{π}{2})$ .
Identify an angle $θ$ in this interval such that $tan θ = - 3$ .
Since $tan (- \frac{π}{3}) = - 3$ and $- \frac{π}{3} \in (- \frac{π}{2}, \frac{π}{2})$ , the required principal value is $- \frac{π}{3}$ .

Common mistake: Choosing

\frac{2 π}{3}

which lies outside the principal range.

Concept tested: Principal value of inverse tangent

Published 4 September 2026 · How this solution was prepared and checked

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Find the principal value of tan−1(−3​).

Step-by-step solution

Find the principal value of $tan^{- 1} (- 3)$ .