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

Determine order and degree (if defined) of differential equation ${\left( {\frac{{ds}}{{dt}}} \right)^4} + 3s\frac{{{d^2}s}}{{d{t^2}}} = 0$

Evaluate the determinant $\left|\begin{array}{cc}x^2-x+1 & x-1 \\ x+1 & x+1\end{array}\right|$

Classify time period as scalar and vector quantities.

Find the area of the region bounded by the curve $y=m x, x$-axis and the ordinates $x=0$ and $x=4$.

Let $T$ be the set of all triangles in a plane with $R$ a relation in $T$ given by
$R = {(T_1, T_2) : T_1}$ is congruent to ${T_2}.$
Show that $R$ is an equivalence relation.

If $\sin ^{-1} x=\frac{\pi}{3}$ then write the value of $\cos ^{-1} x$

Show that the function $f: N $ to $N,$ given by $f (x) = 2x,$ is one$-$one but not onto.

How many number of arbitrary constants in the general solution of a differential equation of fourth order.

The area bounded by the curve y = x|x|, x-axis and the ordinates x = -1 and x = 1 is given by

Compute the following sums:
$\begin{bmatrix}3&-2\\1&4\end{bmatrix}+\begin{bmatrix}-2&4\\1&3\end{bmatrix}$