Find all solutions in the interval 0° ≤ 𝜃 < 360°

Question

tan 𝜃 + 2 cos 𝜃 tan 𝜃 =0

Answer 1

Hello Ashtin,

You can factor out tan θ and get the following equation: tan θ (1 + 2 cosθ) = 0

Now you have 2 equations to solve separately:

1. tan θ= 0 which is possible when θ = 0° or 180° (check your unit circle)
2. 1 + 2 cosθ = 0 ----> 2cosθ = -1 ---> cosθ= -1/2

cosθ is negative in Quadrants 2 and 3, so one solution will be in Q2, the other in Q3: 120° and 240°

Combine the solutions from the 1st and 2nd equations and your solution set is: 0°, 120°, 180°, 240°