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→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Find the vector equation of the plane with intercepts $\text{3, -4 and 2 on } x, y \text{ and } z-\text{axis}$ respectively.

Evaluate the following:
$\tan^{-1}(\tan4)$

Sketch the graph of $\text{y}=\sqrt{\text{x}+1}$ in [0, 4] and determine the area of the region enclosed by the curve, the x-axis and the lines x = 0, x = 4.

Find the length of perpendicular drawn from origin to plane $2 x+3 y+5 z-8=0$

If two events $A$ and $B$ are such that $P(A)=\frac{1}{4}, P(B)=\frac{1}{2}$ and $P(A \cap B)=\frac{1}{8}$, then find the value of $P\left(A^{\prime} \cap B^{\prime}\right)$

Differentiate the following w.r.t.x: $\log(\log\text{x}),\text{x}>1$

Find: $\int \sin 2 x \cos 3 x d x$

If $\big|\vec{\text{a}} \times \vec{\text{b}}\big|^{2} + \big|\vec{\text{a}} . \vec{\text{b}}\big|^{2} = 400 \text{ and } \big|\vec{\text{a}}\big| = 5,$ then write the value of $\big|\vec{\text{b}}\big|.$

Prove $\int_{0}^{1} x e^{x} d x=1$

A homogeneous equation of the form $\frac{{dy}}{{dx}} = h\left( {\frac{x}{y}} \right)$ can be solved by making the substitution