What is the general solution for sin(θ)= 8/12 ?

The general solution for sin(θ)= 8/12 is θ=0.72972…+2pin,θ=pi-0.72972…+2pin

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sin(θ)= 8/12

sin (θ) = \frac{8}{12}

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{8}{12}

Cancel the common factor:

4

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

y, \int x d x = csc^{2} (\frac{y}{2})

sec (x) + 2 = 0, - π \leq x \leq \frac{3 π}{2}

sin^{2} (x) = \frac{1}{9}

2 sin^{2} (x) + sin (x) = \frac{1}{2}

tan (x) = 0.327

What is the general solution for sin(θ)= 8/12 ?
The general solution for sin(θ)= 8/12 is θ=0.72972…+2pin,θ=pi-0.72972…+2pin