What is the general solution for sin(θ)= 12/17 ?

The general solution for sin(θ)= 12/17 is θ=0.78366…+2pin,θ=pi-0.78366…+2pin

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sin(θ)= 12/17

sin (θ) = \frac{12}{17}

θ = 0.78366 \dots + 2 πn, θ = π - 0.78366 \dots + 2 πn

Degrees

θ = 44.90087 \dots^{\circ} + 36 0^{\circ} n, θ = 135.09912 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (θ) = \frac{12}{17}

Apply trig inverse properties

sin (θ) = \frac{12}{17}

General solutions for

sin (θ) = \frac{12}{17}

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

θ = arcsin (\frac{12}{17}) + 2 πn, θ = π - arcsin (\frac{12}{17}) + 2 πn

θ = arcsin (\frac{12}{17}) + 2 πn, θ = π - arcsin (\frac{12}{17}) + 2 πn

Show solutions in decimal form

θ = 0.78366 \dots + 2 πn, θ = π - 0.78366 \dots + 2 πn

\frac{41412}{194874} = tan (θ)

4 cos (β) sin (β) + 2 sin (β) - 2 cos (β) - 1 = 0

5 sin^{2} (x) = cos (x)

cos (x) = \frac{1 + cos ( x )}{2}

cos (x) = \frac{1 + cos ( x )}{2}

What is the general solution for sin(θ)= 12/17 ?
The general solution for sin(θ)= 12/17 is θ=0.78366…+2pin,θ=pi-0.78366…+2pin