Question

Find the values of $\cos \theta$ and $\tan \theta$, given $\sin \theta =\frac{8}{17}$ and $\theta$ is in quadrant $1$.

Answer 1

We are given, $\sin \theta =\frac{8}{17}$

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

$\cos \theta =\sqrt{1-{\left(\frac{8}{17}\right)}^2}$

$\cos \theta =\sqrt{1-\frac{64}{289}}=\sqrt{\frac{289-64}{289}}$

$\cos \theta =15/17$

$\tan \theta =\frac{\sin \theta }{\cos \theta }=\frac{8}{17}\times \frac{17}{15}=\frac{8}{15}$