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

Evaluate the definite integral $\int\limits_0^{\frac{\pi }{2}} {{{\cos }^2}x dx} $

Let A and B be two independent events such that P(A) = p₁ and P(B) = p₂. Describe in words the events whose probabilities are:
(1 - p₁)p₂.

If $\text{f(x)}=\log_\text{e}(\log_\text{e}\text{x}),$ then write the value of f'(e).

Evaluate the following:
$\sec^{-1}\Big(\sec\frac{7\pi}{3}\Big)$

Find the intervals in which the function f given by f(x) = 2x² – 3x is decreasing.

The radius of a circle is increasing uniformly at the rate of $3 cm / s$. Find the rate at which the area of the circle is increasing when the radius is 10 cm .

Determine the order and degree of the following differential equations. state also whether they are linear or non linear.
${3}\sqrt{\frac{\text{d}^2\text{y}}{\text{dx}^2}}=\sqrt{\frac{\text{dy}}{\text{dx}}}$

Prove that $\text{f(x)}=\begin{cases}\frac{\text{x}-|\text{x}|}{\text{x}},&\text{x}\neq0\\2,&\text{x}=0\end{cases}$ is discontinuous at x = 0.

Evaluate the following:
$\sec^{-1}\Big\{\sec\Big(-\frac{7\pi}{3}\Big)\Big\}$

Write the identity element for the binary operation * on the set R₀ of all non-zero real numbers by the rule $\text{a}\times\text{b}=\frac{\text{ab}}{2}$ for all a, b ∈ R₀.