What is the general solution for sin(θ)= 175/214 ?

The general solution for sin(θ)= 175/214 is θ=0.95750…+2pin,θ=pi-0.95750…+2pin

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sin(θ)= 175/214

sin (θ) = \frac{175}{214}

θ = 0.95750 \dots + 2 πn, θ = π - 0.95750 \dots + 2 πn

Degrees

θ = 54.86088 \dots^{\circ} + 36 0^{\circ} n, θ = 125.13911 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (θ) = \frac{175}{214}

Apply trig inverse properties

sin (θ) = \frac{175}{214}

General solutions for

sin (θ) = \frac{175}{214}

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

θ = arcsin (\frac{175}{214}) + 2 πn, θ = π - arcsin (\frac{175}{214}) + 2 πn

θ = arcsin (\frac{175}{214}) + 2 πn, θ = π - arcsin (\frac{175}{214}) + 2 πn

Show solutions in decimal form

θ = 0.95750 \dots + 2 πn, θ = π - 0.95750 \dots + 2 πn

2 \cdot cos^{2} (x) - cos (x) - 1 = 0, 0 \leq x \leq π

2 cos^{3} (x) - cos^{2} (x) = 0

sin^{2} (x) - 2 = sin (x)

arccosh (x) = \frac{2 π}{7}

arccosh (x) = \frac{2 π}{5}

What is the general solution for sin(θ)= 175/214 ?
The general solution for sin(θ)= 175/214 is θ=0.95750…+2pin,θ=pi-0.95750…+2pin