What is the general solution for 2-3sin(θ+(4pi)/3)=2 ?

The general solution for 2-3sin(θ+(4pi)/3)=2 is θ=2pin-(4pi)/3 ,θ=pi+2pin-(4pi)/3

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2-3sin(θ+(4pi)/3)=2

2 - 3 sin (θ + \frac{4 π}{3}) = 2

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

Solution steps

2 - 3 sin (θ + \frac{4 π}{3}) = 2

Subtract

2

from both sides

2 - 3 sin (θ + \frac{4 π}{3}) - 2 = 2 - 2

Simplify

- 3 sin (θ + \frac{4 π}{3}) = 0

Divide both sides by

- 3

sin (θ + \frac{4 π}{3}) = 0

General solutions for

sin (θ + \frac{4 π}{3}) = 0

θ + \frac{4 π}{3} = 0 + 2 πn, θ + \frac{4 π}{3} = π + 2 πn

Solve

θ + \frac{4 π}{3} = 0 + 2 πn : θ = 2 πn - \frac{4 π}{3}

Solve

θ + \frac{4 π}{3} = π + 2 πn : θ = π + 2 πn - \frac{4 π}{3}

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

tan (θ) = \frac{2}{6}

4 + 3 cos (x) = 0

3 sin^{2} (θ) - sin (θ) - 4 = 0

tan^{2} (x) = sin (x) sec (x)

cos (x) = - 6544

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