Teresa Manning

2023-03-11

The principal solution of the equation $\mathrm{sin}x=1/2$ that is less than $\frac{\pi }{2}$ is
A)$\frac{\pi }{3}$
B)$\frac{\pi }{2}$
C)$\frac{\pi }{6}$

### Answer & Explanation

fodheargnl0

The right answer is C $\frac{\pi }{6}$
We have equation is:
$\mathrm{sin}x=\frac{1}{2}$
$⇒\mathrm{sin}x=\mathrm{sin}\frac{\pi }{6}$
Hence, one principal solution of the equation is $\frac{\pi }{6}$
Also, $\mathrm{sin}x=\mathrm{sin}\left(\pi -x\right)$
Hence, $\mathrm{sin}\frac{\pi }{6}=\mathrm{sin}\left(\pi -\frac{\pi }{6}\right)$
Or, $\mathrm{sin}\frac{\pi }{6}=\mathrm{sin}\frac{5\pi }{6}$
Therefore, the other main answer to the equation is $\frac{5\pi }{6}$.
The principal solution which is less than $\frac{\pi }{2}$ is $\frac{\pi }{6}$

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