Question

If $\cos A=\frac{12}{13}$, then find $\sin A$ and $\tan A$.

Answer 1

In a triangle,

$\sin A=\sqrt{1-\left({\cos }^{2}A\right)}$

$\Rightarrow \sin A=\sqrt{1-{\left(\frac{12}{13}\right)}^2}$

$\Rightarrow \sin A=\sqrt{\frac{169-144}{169}}$

$\Rightarrow \sin A=\frac{5}{13}$

And also $\tan A=\frac{\sin A}{\cos A}=\frac{\frac{5}{13}}{\frac{12}{13}}=\frac{5}{12}$