Cos x = -1/2 and cot x>0

Question

Solve please

Answer 1

Solving cos(x) = -1/2 using the unit circle, then x = 2π/3 + 2πn, 4π/3 + 2πn

Given cot(x)>0, then tan(x)>0 since cot(x)=1/tan(x), which means we are either in Quadrant I or Quadrant III. As 4π/3 is in Quadrant III, then that is our solution.

Therefore, the solution for x in the equation cos(x) = -1/2 given cot(x)>0 is 4π/3.

Hope this helped!

Answer 2