Solve the following trig equation for the interval [0,2pie]

Question

Tan = -2

 

Answer 1

Use the inverse tangent function. Since tangent is negative in the 2nd and 4th quadrants, you have

 

x₁ = π - tan^-1(2)

x₂ = 2π - tan^-1(2)

Answer 2

tan θ = -2, θ in QII or QIV

tan^-1 -2 = θ

θ ∈ {296.565°, 116.565}