# How do you find the other trigonometric functions given tantheta=2/3, sectheta=sqrt13/3?

Oct 30, 2017

the other trigonometric functions are $\sin \theta = \frac{2}{\sqrt{13}}$
$\cos \theta = \frac{3}{\sqrt{13}}$ $\cot \theta = \frac{3}{2}$ $\cos e c \theta = \frac{\sqrt{13}}{2}$
it is given that $\sec \theta = \frac{\sqrt{13}}{2} \Rightarrow \cos \theta = \frac{3}{\sqrt{13}}$
$\tan \theta = \frac{2}{3}$ since $\tan \theta = \sin \frac{\theta}{\cos} \theta \Rightarrow \frac{2}{3} = \sin \theta \left(\frac{\sqrt{13}}{3}\right)$
$\Rightarrow \sin \theta = \frac{2}{\sqrt{13}}$ since $\cos e c \theta = \frac{1}{\sin} \theta \Rightarrow \cos e c \theta = \frac{\sqrt{13}}{2}$
since $\cot \theta = \frac{1}{\tan} \theta \Rightarrow \cot \theta = \frac{3}{2}$