First slide

Properties of ITF

Question

$If x = \sin^{- 1} (\sin 10) and y = \cos^{- 1} (\cos 10),$ then y - x is equal to

Moderate

A

0
B

10
C

7 $π$
D

$π$

Solution

The graph of y = sin^-1(sin x) is
$∴ x = \sin^{- 1} (\sin 10) = - 10 + 3 π . . . . (i)$
and the graph of y = cos^-1(cos x) is

$∴ y = \cos^{- 1} (\cos 10) = - 10 + 4 π . . . (ii)$
Now, from Eqs. (i) and (ii),
$y - x = (- 10 + 4 π) - (- 10 + 3 π) = π$

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