What is the general solution for 3sin^2(θ)+3sin(θ)-6=-4sin(θ) ?

The general solution for 3sin^2(θ)+3sin(θ)-6=-4sin(θ) is θ=0.72972…+2pin,θ=pi-0.72972…+2pin

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3sin^2(θ)+3sin(θ)-6=-4sin(θ)

3 sin^{2} (θ) + 3 sin (θ) - 6 = - 4 sin (θ)

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

Solution steps

3 sin^{2} (θ) + 3 sin (θ) - 6 = - 4 sin (θ)

Solve by substitution

sin (θ) = \frac{2}{3}, sin (θ) = - 3

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

sin (θ) = - 3 :

No Solution

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 (4 x) - cos (3 x) = sin (2 x)

sin (x) cos (x) = \frac{1}{2} tan (x)

x, 2 sec^{2} (x) + tan^{2} (x) - 3 = 0

5 sin (\frac{θ}{2}) = 5 cos (\frac{θ}{2})

tan (x) = \frac{80}{50}

What is the general solution for 3sin^2(θ)+3sin(θ)-6=-4sin(θ) ?
The general solution for 3sin^2(θ)+3sin(θ)-6=-4sin(θ) is θ=0.72972…+2pin,θ=pi-0.72972…+2pin