What is the general solution for (2-3sin(θ))/2 =-3sin(θ) ?

The general solution for (2-3sin(θ))/2 =-3sin(θ) is θ=-0.72972…+2pin,θ=pi+0.72972…+2pin

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(2-3sin(θ))/2 =-3sin(θ)

\frac{2 - 3 sin ( θ )}{2} = - 3 sin (θ)

θ = - 0.72972 \dots + 2 πn, θ = π + 0.72972 \dots + 2 πn

Solution steps

\frac{2 - 3 sin ( θ )}{2} = - 3 sin (θ)

Solve by substitution

sin (θ) = - \frac{2}{3}

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

Combine all the solutions

θ = arcsin (- \frac{2}{3}) + 2 πn, θ = π + arcsin (\frac{2}{3}) + 2 πn

Show solutions in decimal form

θ = - 0.72972 \dots + 2 πn, θ = π + 0.72972 \dots + 2 πn

sin (2 x) = \frac{- 3}{2}

x, arctan (x) = \frac{π y}{4}

1 = 4 sin (x)

tan (x) = \frac{45}{67}

k, 1.5 = 6 (- cos (\frac{k}{2}) + 1)

What is the general solution for (2-3sin(θ))/2 =-3sin(θ) ?
The general solution for (2-3sin(θ))/2 =-3sin(θ) is θ=-0.72972…+2pin,θ=pi+0.72972…+2pin