Question

Find all solutions of the equation in the interval (0,2π) cot theta +root 3 = 0

Answer 1

Answer:

θ = 5π/6 rad and 11π/6 rad

Step-by-step explanation:

Given the expression cotθ+√3=0

Subtract √3 from both sides

cotθ+√3-√3=0-√3

cotθ = -√3

Since cotθ = 1/tanθ

1/tanθ = -√3

Reciprocate both sides:

tanθ = -1/√3

θ = tan^-1(-1/√3)

θ = -30°

Since the angle is negative, and tanθ is negative in the second and fourth quadrant.

In the second quadrant;

θ = 180-30

θ = 150°

Since 180° = πrad

150° = 150π/180

150° = 5π/6 rad

In the fourth quadrant;

θ = 360-30

θ = 330°

Since 180° = πrad

330° = 330π/180

330° = 11π/6 rad

Hence the solutions are 5π/6 rad and 11π/6 rad.