Answer:
θ = 5π/6 or 11π/6
Step-by-step explanation:
It is required to find the value of [tex]Cot^{-1}(-\sqrt{3} )[/tex]
Let [tex]\theta = Cot^{-1}(-\sqrt{3} )[/tex]
So, cot θ = -√3 ⇒ tan θ = 1/cot θ = -1/√3
So, from the basic angles, we should know that
tan 30 = 1/√3 ⇒ Cot 30 = √3
But the given cot function is negative, so the required angle lies at the second quarter or at the fourth quarter.
So, θ = -30°
OR θ = 330° or 150°
converting to radians by multiplying at π/180
∴ θ = 330 * π/180 = 11π/6
Or θ = 150 * π/180 = 5π/6
So, θ = 5π/6 or 11π/6
