Question

If $\cos \theta =\frac{4}{5}$, find $\sin \theta$ and $\cot \theta$.

Answer 1

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

We know,

$\Rightarrow$ ${\sin }^2\theta +{\cos }^2\theta =1$

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

$\Rightarrow$ $\sin \theta =\sqrt{1-{\left(\frac{4}{5}\right)}^2}$

$\Rightarrow$ $\sin \theta =\sqrt{1-\frac{16}{25}}$

$\Rightarrow$ $\sin \theta =\sqrt{\frac{9}{25}}$

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

Now,

$\Rightarrow$ $\cot \theta =\frac{\cos \theta }{\sin \theta }$

$\Rightarrow$ $\cot \theta =\frac{\cos \theta }{\sin \theta }$

$\Rightarrow$ $\cot \theta =\frac{\frac{4}{5}}{\frac{3}{5}}$

$\Rightarrow$ $\cot \theta =\frac{4}{3}$