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

The general solution for 3sin^2(θ)-2sin(θ)=2 is θ=-0.58066…+2pin,θ=pi+0.58066…+2pin

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3sin^2(θ)-2sin(θ)=2

3 sin^{2} (θ) - 2 sin (θ) = 2

θ = - 0.58066 \dots + 2 πn, θ = π + 0.58066 \dots + 2 πn

Solution steps

3 sin^{2} (θ) - 2 sin (θ) = 2

Solve by substitution

sin (θ) = \frac{1 + 7}{3}, sin (θ) = \frac{1 - 7}{3}

sin (θ) = \frac{1 + 7}{3} :

No Solution

sin (θ) = \frac{1 - 7}{3} : θ = arcsin (\frac{1 - 7}{3}) + 2 πn, θ = π + arcsin (- \frac{1 - 7}{3}) + 2 πn

Combine all the solutions

θ = arcsin (\frac{1 - 7}{3}) + 2 πn, θ = π + arcsin (- \frac{1 - 7}{3}) + 2 πn

Show solutions in decimal form

θ = - 0.58066 \dots + 2 πn, θ = π + 0.58066 \dots + 2 πn

2 - sin (x) tan (x) = cos (x)

tan (2 x - \frac{n}{4}) = - 1, 0^{\circ} < x \leq 36 0^{\circ}

2 sin^{2} (θ) = cos^{2} (θ)

- cos (x) = - sin^{2} (x) - 1, (0, 2 π)

x, y + arctan (\frac{y}{x}) = 0

What is the general solution for 3sin^2(θ)-2sin(θ)=2 ?
The general solution for 3sin^2(θ)-2sin(θ)=2 is θ=-0.58066…+2pin,θ=pi+0.58066…+2pin