SATHEE: Inverse Circular Functions 3 Question 5

Inverse Circular Functions 3 Question 5

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

(2019 Main, 9 Jan II)

(a) 0

(b) 10

(d) $π$

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Answer:

Correct Answer: 5. (d)

Solution:

The graph of $y = \sin^{- 1} (\sin x)$ is

$∴ x = \sin^{- 1} (\sin 10) = - 10 + 3 π$

and the graph of $y = \cos^{- 1} (\cos x)$ is

$∴ y = \cos^{- 1} (\cos 10) = - 10 + 4 π$

Now, from Eqs. (i) and (ii),

$y - x = (- 10 + 4 π) - (- 10 + 3 π) = π$

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Inverse Circular Functions 3 Question 5

5. If x=sin−1⁡(sin⁡10) and y=cos−1⁡(cos⁡10), then y−x is equal to

Answer:

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