What is the general solution for 16sin^2(θ)=12 ?

The general solution for 16sin^2(θ)=12 is θ= pi/3+2pin,θ=(2pi)/3+2pin,θ=(4pi)/3+2pin,θ=(5pi)/3+2pin

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16sin^2(θ)=12

16 sin^{2} (θ) = 12

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

16 sin^{2} (θ) = 12

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

tan (θ) = - \frac{57}{9}

sin^{2} (x) = \frac{2}{3}

sin (4 y) + sin (6 y) + cos (y) = 0

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

x, ln (y) = arctan (x) + C

What is the general solution for 16sin^2(θ)=12 ?
The general solution for 16sin^2(θ)=12 is θ= pi/3+2pin,θ=(2pi)/3+2pin,θ=(4pi)/3+2pin,θ=(5pi)/3+2pin