Question

If $sin\theta =\frac{3}{5}$ and $\theta$ is acute angle, find
$cos\theta$.

Answer 1

$\sin \theta =\frac{3}{5}$

$\cos \theta =\sqrt{1-{\sin }^2\theta }$

$=\sqrt{1-{\left(\frac{3}{5}\right)}^2}$

$=\sqrt{1-\frac{9}{25}}$

$=\sqrt{\frac{25-9}{25}}$

$=\sqrt{\frac{16}{25}}$

$=\pm \frac{4}{5}$

Since $\theta$ is acute, the $\theta$ is in first quadrant.

$\therefore \cos \theta =\frac{4}{5}$