What is the general solution for 6-2sin(θ)-8sin^2(θ)=0 ?

The general solution for 6-2sin(θ)-8sin^2(θ)=0 is θ=(3pi)/2+2pin,θ=0.84806…+2pin,θ=pi-0.84806…+2pin

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6-2sin(θ)-8sin^2(θ)=0

6 - 2 sin (θ) - 8 sin^{2} (θ) = 0

θ = \frac{3 π}{2} + 2 πn, θ = 0.84806 \dots + 2 πn, θ = π - 0.84806 \dots + 2 πn

Solution steps

6 - 2 sin (θ) - 8 sin^{2} (θ) = 0

Solve by substitution

sin (θ) = - 1, sin (θ) = \frac{3}{4}

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

sin (θ) = \frac{3}{4} : θ = arcsin (\frac{3}{4}) + 2 πn, θ = π - arcsin (\frac{3}{4}) + 2 πn

Combine all the solutions

θ = \frac{3 π}{2} + 2 πn, θ = arcsin (\frac{3}{4}) + 2 πn, θ = π - arcsin (\frac{3}{4}) + 2 πn

Show solutions in decimal form

θ = \frac{3 π}{2} + 2 πn, θ = 0.84806 \dots + 2 πn, θ = π - 0.84806 \dots + 2 πn

cos (2 θ) = cos (3 θ)

θ, 2 sin (θ) = 1.5

cos (θ) = - 2109

x, cos (x) (cos (x) - sin (x)) = 0

sin (x) = 0.72555

What is the general solution for 6-2sin(θ)-8sin^2(θ)=0 ?
The general solution for 6-2sin(θ)-8sin^2(θ)=0 is θ=(3pi)/2+2pin,θ=0.84806…+2pin,θ=pi-0.84806…+2pin