What is the general solution for sin(θ)= 2/3 ?

The general solution for sin(θ)= 2/3 is θ=0.72972…+2pin,θ=pi-0.72972…+2pin

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sin(θ)= 2/3

sin (θ) = \frac{2}{3}

θ = 0.72972 \dots + 2 πn, θ = π - 0.72972 \dots + 2 πn

Degrees

θ = 41.81031 \dots^{\circ} + 36 0^{\circ} n, θ = 138.18968 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (θ) = \frac{2}{3}

Apply trig inverse properties

sin (θ) = \frac{2}{3}

General solutions for

sin (θ) = \frac{2}{3}

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

θ = arcsin (\frac{2}{3}) + 2 πn, θ = π - arcsin (\frac{2}{3}) + 2 πn

θ = arcsin (\frac{2}{3}) + 2 πn, θ = π - arcsin (\frac{2}{3}) + 2 πn

Show solutions in decimal form

θ = 0.72972 \dots + 2 πn, θ = π - 0.72972 \dots + 2 πn

sin (2 θ) = 0

tan (x) = \frac{3}{2}

cos (4 x) = 0

sin^{3} (x) = sin (x)

cos (x) - sin (x) = 1

What is the general solution for sin(θ)= 2/3 ?
The general solution for sin(θ)= 2/3 is θ=0.72972…+2pin,θ=pi-0.72972…+2pin