Find the value of the expression ^ - 1 ; ( 2 3 ). - Vidyadip

Question

Find the value of the expression ${\sin ^{ - 1}}\;\sin \left( {\frac{{2\pi }}{3}} \right)$.

✓

Answer

${\sin ^{ - 1}}\left( {\sin \frac{{2\pi }}{3}} \right) \ne \frac{{2\pi }}{3}$
as $\frac{{2\pi }}{3} \in \left[ {\frac{{ - \pi }}{2},\frac{\pi }{2}} \right]$
${\sin ^{ - 1}}\left( {\sin \frac{{2\pi }}{3}} \right) = {\sin ^{ - 1}}\left[ {{{\sin }^{ - 1}}\left( {\pi - \frac{\pi }{3}} \right)} \right]$
$= {\sin ^{ - 1}}\left[ {\sin \left( {\frac{\pi }{3}} \right)} \right]$
$ = \frac{\pi }{3}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "1 Marks Question" from Inverse Trigonometric Functions→Inverse Trigonometric Functions — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Find the transpose of the matrix: $\left[\begin{array}{c} {5} \\ {\frac{1}{2}} \\ {-1} \end{array}\right]$

The vector directed from A to B and joining the points $A (1,2,2)$ and $B (2,3,1)$ is :

Construct a 4 × 3 matrix whose element are:
$\text{a}_\text{ij}=\frac{\text{i}-\text{j}}{\text{i}+\text{j}}$

A fair coin is tossed 8 times, find the probability of.
exactly 5 heads.

Evaluate $\text{P}(\text{A}\cap\text{B})\ \text{if}\ 2\text{P}(\text{A})=\text{P}(\text{B})=\frac{5}{13}\ \text{and}\ \text{P}(\text{A}|\text{B})=\frac{2}{5}.$

Let * be a 'binary' operation on N given by a * b = LCM (a, b) for all a, b $\in$ N. Find 5 * 7.

State which of the following are not the probability distributions of a random variable. Give reasons for your answer.

X	0	1	2	3	4
P(X)	0.1	0.5	0.2	-1	0.3

A person has undertaken a construction job. The probabilities are 0.65 that there will be strike, 0.80 that the construction job will be completed on time if there is no strike, and 0.32 that the construction job will be completed on time if there is a strike. Determine the probability that the construction job will be completed on time.

Determine order and degree $($if defined$)$ of differential equation: $y" + (y')^2 + 2y = 0$

Evaluate $\int_{-1}^{\frac{3}{2}}|x \sin \ (\pi x)| d x$