First slide

Properties of ITF

Question

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

Moderate

A

10
B

$10 - 3 π$
C

$3 π - 10$
D

none of these

Solution

We have,
$3 π < 10 < 3 π + \frac{π}{2}$
$\begin{array}{l} \Rightarrow 0 < 10 - 3 π < \frac{π}{2} \\ \Rightarrow - \frac{π}{2} < 3 π - 10 < 0 \Rightarrow \sin^{- 1} (\sin (3 π - 10)) = 3 π - 10 \end{array}$

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