Question

Given : $4sin\Theta =3cos\Theta$; find the value of sin$\Theta$

• A. $\frac{3}{5}$
• B. $\frac{2}{7}$
• C. $\frac{7}{5}$
• D. $\frac{3}{7}$

Answer 1

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

$4\sin \Theta =3\cos \Theta$
$\tan \Theta =\frac{3}{4}$
$\tan \Theta =\frac{P}{B}=\frac{3}{4}$
Using Pythagoras Theorem,
$H^2=P^2+B^2$
$H^2=3^2+4^2$
$H^2=5^2$
$H=5$
$\sin \Theta =\frac{P}{H}=\frac{3}{5}$