# How do you determine cottheta given tantheta=sqrt3/4, 0<theta<pi/2?

Nov 12, 2016

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

#### Explanation:

Consider the following $\textcolor{b l u e}{\text{trigonometric identity}}$

$\textcolor{\mathmr{and} a n \ge}{\text{Reminder }} \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{\cot \theta = \frac{1}{\tan} \theta} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$0 < \theta < \frac{\pi}{2}$ informs us that we are in the first quadrant where all trig ratios are positive.

$\Rightarrow \cot \theta = \frac{1}{\frac{\sqrt{3}}{4}} = 1 \times \frac{4}{\sqrt{3}} = \frac{4}{\sqrt{3}}$