First slide

Properties of ITF

Question

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

Moderate

A

$3 π - 10$
B

$10 - 3 π$
C

$3 π + 10$
D

$4 π - 10$

Solution

We know that $\sin^{- 1} (\sin θ) = θ, if - \frac{π}{2} \leq θ \leq \frac{π}{2}$
Here, $θ = 10$ radians which does not lie between $- \frac{π}{2} and \frac{π}{2}$
But, $3 π - θ i.e. 3 π - 10$ lies between $- \frac{π}{2} and \frac{π}{2}$
Also $\begin{array}{l} \sin (3 π - 10) = \sin 10 \\ \sin^{- 1} (\sin 10) = \sin^{- 1} (\sin (3 π - 10)) = 3 π - 10 \end{array}$

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