Question

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

Answer 1

`cottheta=4/sqrt3`

Explanation:

Consider the following `color(blue)"trigonometric identity"`

`color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(cottheta=1/tantheta)color(white)(2/2)|)))`

`0 < theta < pi/2` informs us that we are in the first quadrant where all trig ratios are positive.

`rArrcottheta=1/(sqrt3/4)=1xx4/sqrt3=4/sqrt3`