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The value of  \sin\ \frac{\pi }{6} using half angle identity.

Option: 1

\frac{1}{\sqrt{2}}


Option: 2

-\frac{1}{\sqrt{2}}


Option: 3

\frac{1}{2}


Option: 4

-\frac{1}{2}


Answers (1)

best_answer

Given that,

\sin\ \frac{\pi }{6}
Here,

\frac{A}{2}=\frac{\pi }{6}
A=\frac{\pi }{3}
Using the Half-angle formula,

\sin\left ( \frac{A}{2} \right )=\sqrt{\frac{1-\cos\ A}{2}}
\sin\left ( \frac{\pi }{6} \right )=\sqrt{\frac{1-\cos\ \left ( \frac{\pi }{3} \right )}{2}}
\sin\left ( \frac{\pi }{6} \right )=\sqrt{\frac{\left ( \frac{1}{2} \right )}{2}}
\sin\left ( \frac{\pi }{6} \right )=\frac{1}{2}
 

Posted by

Gaurav

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