What is the general solution for 5sin^2(θ)=2sin(θ) ?

The general solution for 5sin^2(θ)=2sin(θ) is θ=2pin,θ=pi+2pin,θ=0.41151…+2pin,θ=pi-0.41151…+2pin

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5sin^2(θ)=2sin(θ)

5 sin^{2} (θ) = 2 sin (θ)

θ = 2 πn, θ = π + 2 πn, θ = 0.41151 \dots + 2 πn, θ = π - 0.41151 \dots + 2 πn

Solution steps

5 sin^{2} (θ) = 2 sin (θ)

Solve by substitution

sin (θ) = 0, sin (θ) = \frac{2}{5}

sin (θ) = 0 : θ = 2 πn, θ = π + 2 πn

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

Combine all the solutions

θ = 2 πn, θ = π + 2 πn, θ = arcsin (\frac{2}{5}) + 2 πn, θ = π - arcsin (\frac{2}{5}) + 2 πn

Show solutions in decimal form

θ = 2 πn, θ = π + 2 πn, θ = 0.41151 \dots + 2 πn, θ = π - 0.41151 \dots + 2 πn

1 + cos (x) = 0

tan^{2} (θ) = \frac{1}{3}

3 cot (x) - 1 = 0

cos (x) + 1 = - cos (x)

sin (2 θ) = - 1

What is the general solution for 5sin^2(θ)=2sin(θ) ?
The general solution for 5sin^2(θ)=2sin(θ) is θ=2pin,θ=pi+2pin,θ=0.41151…+2pin,θ=pi-0.41151…+2pin