Question

the principal solution of sin tita=1/2is​

Answer 1

$\large </p><p>\bold{ \underline{ \underline{ \: Given : \: \: \: }}}$

$\to$ $\sin( \theta) = \frac{1}{2}$

$\large \bold{ \underline{ \underline{ \: To \: find : \: \: \: }}}$

$\to$ Principal Solution

$\large \bold{ \underline{ \underline{ \: Solution : \: \: \: }}}$

$\to \sin( \theta) = \frac{1}{2} \\ \\ \to \sin( \theta) = \sin( \frac{\pi}{6} ) \\ \\ \to \theta = \frac{\pi}{6}$

$\underline \bold{General \: solution : \: \: }$

$\to$ $\theta = n\pi + {( - 1)}^{n} (\frac{\pi}{6} )$

$\underline \bold{Principal \: solution : \: \: }$

$\to$ $\theta = \frac{\pi}{6} \: , \: \pi - \frac{\pi}{6} \: , \: 2\pi + \frac{\pi}{6} \: ..........$