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

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

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3sin^2(θ)-4=-4sin(θ)

3 sin^{2} (θ) - 4 = - 4 sin (θ)

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

Solution steps

3 sin^{2} (θ) - 4 = - 4 sin (θ)

Solve by substitution

sin (θ) = \frac{2}{3}, sin (θ) = - 2

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

sin (θ) = - 2 :

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

2 cos^{2} (x) - 1 + cos (x) = 0

4 cot (θ) sin (θ) = 2

2 sin (2 x) - 5 tan (2 x) = 0

75 = \frac{120}{4} \cdot cos (\frac{2 \cdot π \cdot x}{360}) + \frac{120}{2}

cot^{2} (x) + 2 = 2 csc (x)

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