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  • Evaluate the value of <img alt="arcsin\left ( \sin\left ( \frac{-11\pi}{3} \right ) \right )" src="https://entrancecorner.oncodecogs.com/gif.latex?arcsin%5Cleft%20%28%20%5Csin%5Cleft%20%28%20%5Cfra

Evaluate the value of arcsin\left ( \sin\left ( \frac{-11\pi}{3} \right ) \right )

Option: 1

\frac{\pi}{3}


Option: 2

\frac{\pi}{6}


Option: 3

\frac{\pi}{4}


Option: 4

\frac{\pi}{2}


Answers (1)

best_answer

Given that,

arcsin\left ( \sin\left ( \frac{-11\pi}{3} \right ) \right )
Let,

arcsin\left ( \sin\left ( y \right ) \right )= y only for -\frac{\pi}{2}\leq y\leq \frac{\pi}{2}.

Transforming the given expression to get,

\sin\left ( \frac{-11\pi}{3} \right )=\sin\left ( \frac{\pi}{3} \right )
arcsin\left (\sin\left ( \frac{-11\pi}{3} \right ) \right )=arcsin\left (\sin\left ( \frac{\pi}{3} \right ) \right )
Now, \frac{\pi}{3} satisfies the condition -\frac{\pi}{2}\leq y\leq \frac{\pi}{2}.


Therefore,

arcsin\left (\sin\left ( \frac{-11\pi}{3} \right ) \right )=\frac{\pi}{3}

Posted by

manish

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