Question
Evaluate the following:
$\sin^{-1}(\sin4)$
$\sin^{-1}(\sin4)$
✓
Answer
We know $\sin\big(\sin^{-1}\theta\big)=\theta$ if $-\frac{\pi}{2}\leq\theta\leq\frac{\pi}{2}$
We have
$=\sin^{-1}(\sin4)$ $=\pi-4$ $\Big(\because\ \sin^{-1}(\sin\theta)=\pi-\theta,\text{if}\ \theta\in\Big[\frac{\pi}{2},\frac{3\pi}{2}\Big]\Big)$Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
The number of arbitrary constants in the general solution of a differential equation of fourth order are:
In triangle ABC, which of the following is not true:
Evaluate the following:
$\cos^{-1}(\cos3)$
→$\cos^{-1}(\cos3)$
Let A be a matrix of order 3 × 4. If R1 denotes the first row of A and C2 denotes its second column, then determine the orders of matrices R1 and C2.
Show the relation R in the set A = {x $\in$ Z : 0 $\leq$ x $\leq$ 12}, given by
R = {(a, b) : |a – b| is a multiple of 4} is an equivalence relation.
Find the set of all elements related to 1 in each case.
→R = {(a, b) : |a – b| is a multiple of 4} is an equivalence relation.
Find the set of all elements related to 1 in each case.
In a triangle OAC, if B is the mid - point of side AC and $\overrightarrow{\text{OA}} = \overrightarrow{\text{a}}, \overrightarrow{\text{OB}} = \overrightarrow{\text{b}}, $ then what is $\overrightarrow{\text{OC}} \text{?}$
→Find the principal value of the following:
$\sin^{-1}\Big(\frac{\sqrt3+1}{2\sqrt2}\Big)$
→$\sin^{-1}\Big(\frac{\sqrt3+1}{2\sqrt2}\Big)$
$\text{If}\ \text{P}(\text{A})=0.8,\ \text{P}(\text{B})=0.5\ \text{and}\ \text{P}(\text{B}|\text{A})=0.4,\ \text{find}:$
$\text{P}(\text{A}\cup\text{B})$
→$\text{P}(\text{A}\cup\text{B})$
Integrate the function x2 log x
Find the intervals in which the function f given by f(x) = 2x3 – 3x2 – 36x + 7 is increasing.