Question

if $\sin \theta =\frac{1}{2}$ and $\cos \theta =-\frac{\sqrt{3}}{2}$ ,then the general value of $\theta is\left(nϵz\right)$

• A. $2n\pi +\frac{5\pi }{6}$
• B. $2n\pi +\frac{\pi }{6}$
• C. $2n\pi +\frac{7\pi }{6}$
• D. $2n\pi +\frac{\pi }{4}$

Answer 1

The correct option is A $2n\pi +\frac{5\pi }{6}$

$sin\theta =\frac{1}{2}$
$cos\theta =\frac{\sqrt{3}}{2}=cos\frac{\pi }{6}$
$\theta =2n\pi \pm \frac{\pi }{6}$

And
$cos\theta =-\frac{\sqrt{3}}{2}$
$\theta =2n\pi \pm \frac{5\pi }{6}$

So, $LCM=\theta =2n\pi \pm \frac{5\pi }{6}$