Question

If $\sin \theta =\frac{3}{4}and\tan \theta =\frac{9}{2},then\cos \theta$ is

• A. $1/6$
• B. $8/27$
• C. $27/8$
• D. $15/4$

Answer 1

The correct option is A $1/6$

$\cos \theta =2{\cos }^2\theta /2-1$

$\therefore \cos \theta /2=\sqrt{\frac{\cos \theta +1}{2}}$

$\therefore \tan \theta =\frac{\sin \theta }{\cos \theta }$

$\therefore \cos \theta =\frac{\sin \theta }{\tan \theta }=\frac{3}{\left(4\right)}\times \frac{\left(2\right)}{\left(9\right)}$

$\therefore \cos \theta =\frac{1}{6}$

$\therefore \cos \theta /2=\sqrt{\frac{1/6+1}{2}}=\sqrt{\frac{7}{12}}$