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What is the value of the arcsin(sin3)

Posted by Harshit Mishra 7 years ago

CBSE > Class 12 > Mathematics

1 answers

Naveen Sharma 7 years ago

Ans.

{tex}arcsin(sin3) = \pi - 3{/tex}

Explanation:

arcsin maps [-1,1] to {tex}\left [-{\pi\over 2}, {\pi\over 2}\right ]{/tex}.

We need to get an angle {tex}x \in \left [-{\pi\over 2}, {\pi\over 2}\right ]{/tex}where sin(x) = sin(3).

Since sin x is symmetric about {tex}x = {\pi\over 2}{/tex}, we have {tex}sin (3) = sin (\pi -3){/tex}. {tex}\pi - 3{/tex} is in {tex}\left [-{\pi\over 2}, {\pi\over 2}\right ]{/tex},

{tex}\therefore we \space have {/tex} {tex}arcsin(sin3) = \pi - 3{/tex}

1Thank You

ANSWER

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