How do you find the solutions on 0≤θ<360?

Question

Find all solutions on 0≤θ<360 of: √3 tanθ - 2sinθtanθ = 0

Answer 1

solve the equation first
√3 tanθ - 2sinθtanθ = 0
√3 tanθ = 2sinθtanθ, now divide by tanθ
√3 = 2 sinθ, now divide by 2
√3 / 2 = sinθ
this is the classic 1-2-√3 triangle,
which is the 30, 60, 90 triangle
notice it has a positive value so the angle must be in the quadrants that have a positive y value
θ = 60, and 120 degree angles

Answer 2

√3 tanθ - 2sinθtanθ = 0
Change to 0<θ<360. Now we can divide by tanθ
√3 - 2sinθ = 0
sin θ = sqrt(3)/2
θ = 60 degrees or 120 degrees

Answer 3

i think you need to solve for this equaion when Q is 0 and 90.