Find the values: ^ -1 ( 2 3 ) - Vidyadip

Question

Find the values:
$\sin^{-1}\bigg(\sin\frac{2\pi}{3}\bigg)$

✓

Answer

For $\sin^{-1}\left(\sin x\right)$ type of problem we have to always check whether the angle is in the principal range or not. This angle must be in the principal range $\bigg[-\frac{\pi}{2},\frac{\pi}{2}\bigg].$
$=\sin^{-1}\bigg(\sin\frac{3\pi-\pi}{3}\bigg)$
$=\sin^{-1}\bigg[\sin\bigg(\pi-\frac{\pi}{3}\bigg)\bigg]$
$=\sin^{-1}\sin\frac{\pi}{3}=\frac{\pi}{3}$

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 "2 Marks" from INVERSE TRIGNOMETRIC FUNCTIONS→INVERSE TRIGNOMETRIC FUNCTIONS — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Write the value of the determinant $\begin{vmatrix}2&3&4\\5&6&8\\6\text{x}&9\text{x}&12\text{x}\end{vmatrix}$

Find a solution of $\frac{{dy}}{{dx}} = y\tan x$ which satisfy the condition y = 1 when x = 0.

Integrate the rational function: $\frac{x}{(x+1)(x+2)}$

If $\text{A}=\begin{bmatrix} 2 & 3 \\ 5 & -2 \end{bmatrix},$ write A^-1 in terms of A.

X is taking up subjects - Mathematics, Physics and Chemistry in the examination. His probabilities of getting grade A in these subjects are 0.2, 0.3 and 0.5 respectively. Find the probability that he gets,
Grade A in no subject.

Evaluate the following integrals:
$\int\frac{\sin\sqrt{\text{x}}}{\sqrt{\text{x}}}\text{ dx}$

If $\vec{\text{a}},\vec{\text{b}}$ are two vectors, then write the truth value of the following statement:

$\vec{\text{a}}=-\vec{\text{b}}\Rightarrow\big|\vec{\text{a}}\big|=\big|\vec{\text{b}}\big|$

Evalute the following integrals:
$\int\sqrt{\frac{1+\cos2\text{x}}{1-\cos2\text{x}}}\text{dx}$

Three shopkeepers A, B and C go to a store to buy stationary. A purchases 12 dozen notebooks, 5 dozen pens and 6 dozen pencils. B purchases 10 dozen notebooks, 6 dozen pens and 7 dozen pencils. Cpurchases 11 dozen notebooks, 13 dozen pens and 8 dozen pencils. A notebook costs 40 paise, a pen costs Rs. 1.25 and a pencil costs 35 paise. Use matrix multiplication to calculate each individual's bill.

If $\begin{vmatrix}2\text{x}&5\\8&\text{x}\end{vmatrix}=\begin{vmatrix}6&-2\\7&3\end{vmatrix},$ write the value of x.