If ^ -1 x=y, then - Vidyadip

MCQ

If $\sin ^{-1} x=y,$ then

A
$-\frac{\pi}{2} < y < \frac{\pi}{2}$
B
$0 \leq \mathrm{y} \leq \pi$
✓
$-\frac{\pi}{2} \leq y \leq \frac{\pi}{2}$
D
$0 < y < \pi$

✓

Answer

Correct option: C.

$-\frac{\pi}{2} \leq y \leq \frac{\pi}{2}$

c
It is given that $\sin ^{-1} x=y$

We know that the range of the principal value branch of $\sin ^{-1}$ is $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$

Therefore, $-\frac{\pi}{2} \leq y \leq \frac{\pi}{2}$

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 STD 12 - 2. inverse trigonometric function→STD 12 - 2. inverse trigonometric function — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

If $A$ and $B$ are any two events such that $P(A)+P(B)-P(A \text { and } B)=P(A),$ then

The range of function $f : R \rightarrow R$, $f(x) = \frac{{{{(x\, + \,1)}^4}}}{{{x^4} + \,1}}$ is

If $A=\left[\begin{array}{ll}x & 0 \\ 1 & 1\end{array}\right]$ and $B=\left[\begin{array}{cc}4 & 0 \\ -1 & 1\end{array}\right]$, then value of $x$ for which $A^2=B$ is

The maximum height is reached in $5$ seconds by a stone thrown vertically upwards and moving under the equation $10s = 10ut -49{t^2}$, where $ s$ is in metre and $t$ is in second. The value of $u$ is ........ $m/\sec $

Let $\vec{a}$ and $\vec{b}$ be the vectors along the diagonal of a parallelogram having area $2 \sqrt{2}$. Let the angle between $\vec{a}$ and $\vec{b}$ be acute. $|\vec{a}|=1$ and $|\vec{a} . \vec{b}|=|\vec{a} \times \vec{b}| .$ If $\vec{c}=2 \sqrt{2}(\vec{a} \times \vec{b})-2 \vec{b}$, then an angle between $\vec{b}$ and $\vec{c}$ is

If two constraints do not intersect in the positive quadrant of the graph, then.

The equation $y^2e^{xy} = 9e^{-3}·x^2$ defines $y$ as a differentiable function of $x$. The value of for $x = - 1$ and $y = 3$ is

$\int_{}^{} {\frac{{10{x^9} + {{10}^x}{{\log }_e}10}}{{{{10}^x} + {x^{10}}}}} \;dx = $

For any two vectors $\vec{a}$ and $\vec{b}$, which of the following statements is always true?

The points of extremum of $\int_0^{{x^2}} {\frac{{{t^2} - 5t + 4}}{{2 + {e^t}}}} \,dt$ are