What is the general solution for 3sin^2(θ)+3sin(θ)+3=7sin(θ)+7 ?

The general solution for 3sin^2(θ)+3sin(θ)+3=7sin(θ)+7 is θ=-0.72972…+2pin,θ=pi+0.72972…+2pin

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3sin^2(θ)+3sin(θ)+3=7sin(θ)+7

3 sin^{2} (θ) + 3 sin (θ) + 3 = 7 sin (θ) + 7

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

Solution steps

3 sin^{2} (θ) + 3 sin (θ) + 3 = 7 sin (θ) + 7

Solve by substitution

sin (θ) = 2, sin (θ) = - \frac{2}{3}

sin (θ) = 2 :

No Solution

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

3 cos (x) = cos (x) - 1

2 sin^{2} (x) - 3 cos (x) - 3 = 0

3 sin^{2} (x) = cos^{2} (x) - 4 cos (x)

cos (x) = 0.9224

- 9 sin^{2} (θ) + 3 cos (θ) - 2 = - 9

What is the general solution for 3sin^2(θ)+3sin(θ)+3=7sin(θ)+7 ?
The general solution for 3sin^2(θ)+3sin(θ)+3=7sin(θ)+7 is θ=-0.72972…+2pin,θ=pi+0.72972…+2pin