What is the general solution for 0=2sin^2(θ)+sqrt(3)sin(θ) ?

The general solution for 0=2sin^2(θ)+sqrt(3)sin(θ) is θ=2pin,θ=pi+2pin,θ=(4pi)/3+2pin,θ=(5pi)/3+2pin

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0=2sin^2(θ)+sqrt(3)sin(θ)

0 = 2 sin^{2} (θ) + 3 sin (θ)

θ = 2 πn, θ = π + 2 πn, θ = \frac{4 π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn

Solution steps

0 = 2 sin^{2} (θ) + 3 sin (θ)

Switch sides

2 sin^{2} (θ) + 3 sin (θ) = 0

Solve by substitution

sin (θ) = 0, sin (θ) = - \frac{3}{2}

sin (θ) = 0 : θ = 2 πn, θ = π + 2 πn

sin (θ) = - \frac{3}{2} : θ = \frac{4 π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn

Combine all the solutions

θ = 2 πn, θ = π + 2 πn, θ = \frac{4 π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn

y, x = arctan (x + y)

2 sin (2 x) = 3 tan (x)

tan (φ) = \frac{1}{3}

sin (θ) \cdot csc (1 8^{\circ}) = 1

tan^{2} (x) + csc^{2} (x) = 3

What is the general solution for 0=2sin^2(θ)+sqrt(3)sin(θ) ?
The general solution for 0=2sin^2(θ)+sqrt(3)sin(θ) is θ=2pin,θ=pi+2pin,θ=(4pi)/3+2pin,θ=(5pi)/3+2pin