alleryThe principal value of $\tan^{-1}(1)$ is
A$\tfrac{\pi}{3}$
B$\tfrac{\pi}{4}$
C$\tfrac{\pi}{2}$
D$\tfrac{\pi}{6}$
Answer & Solution
Correct answer: B. $\tfrac{\pi}{4}$
$\tan^{-1}$ returns values in $\left(-\tfrac{\pi}{2}, \tfrac{\pi}{2}\right)$.
We need $\tan\theta = 1$ with $\theta$ in that range, which gives $\theta = \tfrac{\pi}{4}$.
Keep practising Unit 1A2: Trigonometric Functions & Inverse Trig
Browse all Unit 1A2: Trigonometric Functions & Inverse Trig questions for AP Calculus AB, or explore more Mathematics topics.
Related questions
In a right triangle, for an acute angle θ, sin θ is defined as:A relation $f$ from $A$ to $B$ is a function if every element of $A$ has:The domain of $f(x)= qrt{4-x^2}$ is:If $(x+1,\,y-2)=(3,\,1)$, then $(x,y)$ equals:The domain of $f(x)= qrt{x-1}$ is:The range of the function $f(x)=x^2,\; x\in\mathbb{R}$ is:The domain of the function $f(x)=\dfrac{1}{x-2}$ is:The reciprocal of sin θ is: