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If \sin x > \frac{{1 }}{2}, then which of the following is true

Option: 1

\left ( 2n\pi + \frac{\pi }{3}, 2n\pi + \frac{5\pi }{3} \right )


Option: 2

\left ( 2n\pi + \frac{\pi }{6}, 2n\pi + \frac{5\pi }{6} \right )


Option: 3

\left ( n\pi + \frac{\pi }{6}, n\pi + \frac{5\pi }{6} \right )


Option: 4

None of these


Answers (1)

best_answer

We can solve the inequalities with the help of graphs

trigonometric inequality

\sin x > \frac{1}{2}

In interval [0,2\pi), sin(x) > 1/2 for x lying in (\pi/6 \,, 5\pi/6) 

So, general solution isx\in \left ( 2n\pi + \frac{\pi }{6}, 2n\pi + \frac{5\pi }{6} \right )

 

Posted by

Irshad Anwar

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