What is the general solution for 3csc^2(θ)-4=0 ?

The general solution for 3csc^2(θ)-4=0 is θ= pi/3+2pin,θ=(2pi)/3+2pin,θ=(4pi)/3+2pin,θ=(5pi)/3+2pin

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3csc^2(θ)-4=0

3 csc^{2} (θ) - 4 = 0

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

3 csc^{2} (θ) - 4 = 0

Solve by substitution

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

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

csc (θ) = - \frac{2 3}{3} : 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

sin (x) = \frac{7}{9}

2 cos (t) = 0

10 sin (θ) + 8 = 11

4 cos (2 θ) = 0

\frac{1}{2} = sin (θ)

What is the general solution for 3csc^2(θ)-4=0 ?
The general solution for 3csc^2(θ)-4=0 is θ= pi/3+2pin,θ=(2pi)/3+2pin,θ=(4pi)/3+2pin,θ=(5pi)/3+2pin