−5 tan θ −13 = 4 tan ⁡θ − 6

Answer 1

−5tan θ − 13 = 4tan ⁡θ − 6

Add 5tanθ to both sides and add 6 to both sides to get:

-7 = 9tanθ

Divide both sides by 9 to get:

tanθ = -7/9

Take tan^-1 of both sides to get:

tan^-1(tanθ) = tan^-1(-7/9)

θ = tan^-1(-7/9)

Use you calculator to get:

θ = -37.875° or (in radians), θ = -0.661 radians

Since tan repeats every 180° (or π radians), you can also say θ = 142.125° or, generally, θ = 142.125° + 180°k where "k" is any integer. Or, in radians, θ = 2.481 radians + πk where "k" is any integer