What is the general solution for sin(θ)= 4/9 ?

The general solution for sin(θ)= 4/9 is θ=0.46055…+2pin,θ=pi-0.46055…+2pin

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sin(θ)= 4/9

sin (θ) = \frac{4}{9}

θ = 0.46055 \dots + 2 πn, θ = π - 0.46055 \dots + 2 πn

Solution steps

sin (θ) = \frac{4}{9}

Apply trig inverse properties

θ = arcsin (\frac{4}{9}) + 2 πn, θ = π - arcsin (\frac{4}{9}) + 2 πn

Show solutions in decimal form

θ = 0.46055 \dots + 2 πn, θ = π - 0.46055 \dots + 2 πn

y, x = sec (y)

2 cos^{2} (θ) - cos (θ) - 4 = - 6 cos (θ) - 6

sin (x) + 2 cos (x) = 1

4 tan (2 x) - 4 cot (x) = 0

sin (x) = \frac{24}{25}

What is the general solution for sin(θ)= 4/9 ?
The general solution for sin(θ)= 4/9 is θ=0.46055…+2pin,θ=pi-0.46055…+2pin