Question

Given that $\tan \theta =\frac{5}{12}$ and $\theta$ is an acute angle, find $\sin \theta$ and $\cos \theta$?

Answer 1

$Tan\theta =\frac{opposite}{adjacent}=\frac{5}{12}$

$opposite=5,adjacent=12$

$hypoteneus=\sqrt{5^2+{12}^2}=\sqrt{25+144}=13$

Using phytagoras,$hypoteneus=13$

$Cos\theta =\frac{adjacent}{hypoteneus}=\frac{12}{13}$

$sin\theta =\frac{hypoteneus}{adjacent}=\frac{13}{12}$