The value of ^ - 1 ( 10) is - Vidyadip

MCQ

The value of ${\sin ^{ - 1}}(\sin 10)$ is

A
$10$
B
$10 - 3\pi $
✓
$3\pi - 10$
D
None of these

✓

Answer

Correct option: C.

$3\pi - 10$

c
(c) Since $3\pi < 10 < 3\pi + \frac{\pi }{2}\,\, $

$\Rightarrow \,0 < 10 - 3\pi < \frac{\pi }{2}$

$ \Rightarrow \,\,\frac{{ - \pi }}{2} < 3\pi - 10 < 0$

$ \Rightarrow \,\,{\sin ^{ - 1}}\left\{ {\sin \,(3\pi - 10)} \right\} = 3\pi - 10$.

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 "M.C.Q (1 Marks)" from 2. inverse trigonometric function→2. inverse trigonometric function — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Let $A = \left[ {\begin{array}{*{20}{c}}1&0&0\\5&2&0\\{ - 1}&6&1\end{array}} \right]$, then the adjoint of $ A $ is

Consider $f(x) = \left\{ \begin{array}{l}\frac{{{x^2}}}{{|x|}},\,x \ne 0\\\,\,\,\,\,\,\,0,\,x = 0\end{array} \right.$

Area of a parallelogram whose adjacent sides are represented by the vectors $2 \hat{i}-3 \hat{k}$ and $4 \hat{j}+2 \hat{k}$ is

Let $g(x)=3 f\left(\frac{x}{3}\right)+f(3-x)$ and $f^{\prime \prime}(x)>0$ for all $\mathrm{x} \in(0,3)$. If $\mathrm{g}$ is decreasing in $(0, \alpha)$ and increasing in $(\alpha, 3)$, then $8 \alpha$ is

${d \over {dx}}{\cos ^{ - 1}}\sqrt {\cos x} = $

Consider a rectangle whose length is increasing at the uniform rate of $2\, m/sec$, breadth is decreasing at the uniform rate of $3\, m/sec$ and the area is decreasing at the uniform rate of $5\,m^2/ sec$ . If after some time the breadth of the rectangle is $2\, m$ then the length of the rectangle is ........ $m.$

Choose the correct answer from the given four options:
let $\text{P}(\text{A})=\frac{7}{13},\text{P}(\text{B})=\frac{9}{13}$ and $\text{P}(\text{A}\cup\text{B})=\frac{4}{13}.$ Then $\text{P}\Big(\frac{\text{A'}}{\text{B}}\Big)$ is equal to:

$\frac{6}{13}$
$\frac{4}{13}$
$\frac{4}{9}$
$\frac{5}{9}$

Let $A=\left[\begin{array}{lll}2 & 0 & 1 \\ 1 & 1 & 0 \\ 1 & 0 & 1\end{array}\right], B=\left[B_1, B_2, B_3\right]$, where $B_1$, $\mathrm{B}_2, \mathrm{~B}_3$ are column matrices, and $\mathrm{AB}_1=\left[\begin{array}{l}1 \\ 0 \\ 0\end{array}\right]$, $\mathrm{AB}_2=\left[\begin{array}{l}2 \\ 3 \\ 0\end{array}\right], \mathrm{AB}_3=\left[\begin{array}{l}3 \\ 2 \\ 1\end{array}\right]$ If $\alpha=|B|$ and $\beta$ is the sum of all the diagonal elements of $B$, then $\alpha^3+\beta^3$ is equal to

Let $f(x) = \left\{ {\begin{array}{*{20}{c}}{\,\,\,\,\,\,\,\,\sin x,}&{{\rm{for\,\, }}x \ge 0}\\{1 - \cos x,}&{{\rm{for\,\, }}x \le 0}\end{array}} \right.$ and $g(x) = {e^x}$. Then $(gof)'(0)$ is

The equation x² - x - 2 = 0 in three-dimensional space is represented by:

A pair of parallel planes
A pair of straight lines
A pair of the perpendicular plane
None of these