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

The general solution for 8sin^2(θ)=6 is θ= pi/3+2pin,θ=(2pi)/3+2pin,θ=(4pi)/3+2pin,θ=(5pi)/3+2pin

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8sin^2(θ)=6

8 sin^{2} (θ) = 6

θ = \frac{π}{3} + 2 πn, θ = \frac{2 π}{3} + 2 πn, θ = \frac{4 π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn

Solution steps

8 sin^{2} (θ) = 6

Solve by substitution

sin (θ) = \frac{3}{2}, sin (θ) = - \frac{3}{2}

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

sin (θ) = - \frac{3}{2} : θ = \frac{4 π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn

Combine all the solutions

θ = \frac{π}{3} + 2 πn, θ = \frac{2 π}{3} + 2 πn, θ = \frac{4 π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn

72 sin^{2} (x) = 72 - 36 cos (x)

3 cos^{2} (x) - 4 cos (x) + 1 = 0

cos (x) = 0.1

3 tan (x) = 2.4568

cos (x) = 1.5

What is the general solution for 8sin^2(θ)=6 ?
The general solution for 8sin^2(θ)=6 is θ= pi/3+2pin,θ=(2pi)/3+2pin,θ=(4pi)/3+2pin,θ=(5pi)/3+2pin