Question

If $\cos \theta =\frac{4}{5}$, then $\sin \theta =......$ and $\tan \theta =......$

• A. $\frac{3}{5},\frac{3}{4}$
• B. $\frac{5}{3},\frac{4}{3}$
• C. $\frac{2}{3},\frac{4}{5}$
• D. None of these

Answer 1

The correct option is A $\frac{3}{5},\frac{3}{4}$

1) Using ${\sin }^2\theta +{\cos }^2\theta =1$
${\sin }^2\theta +{\left(\frac{4}{5}\right)}^2=1$
${\sin }^2\theta =1-\frac{16}{25}=\frac{9}{25}$
$\therefore \sin \theta =\frac{3}{5}$

2) $\tan \theta =\frac{\sin \theta }{\cos \theta }$
$=\frac{\frac{3}{5}}{\frac{4}{5}}=\frac{3\times 5}{4\times 5}$
$\therefore \tan \theta =\frac{3}{4}$

Hence correct option is 'A'