Question

If $\cos \theta +\left(\frac{1}{\sqrt{3}}\right)\sin \theta =\frac{2}{\sqrt{3}}$, then find $\theta$ in circular measure.

Answer 1

$\cos \theta +\left(\frac{1}{\sqrt{3}}\right)\sin \theta =\frac{2}{\sqrt{3}}$

$\left(\frac{\sqrt{3}}{2}\right)\cos \theta +\left(\frac{1}{2}\right)\sin \theta =1$

$sin{60}^{o}cos\theta +\sin \theta cos{60}^o=1$

$sin({60}^o+\theta )=sin{90}^o$

${60}^o+\theta ={90}^o$

$\theta ={30}^o$

$\theta =\frac{{\pi }^c}{6}$.