What is the general solution for sin(θ)=0.61927 ?

The general solution for sin(θ)=0.61927 is θ=0.66781…+2pin,θ=pi-0.66781…+2pin

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sin(θ)=0.61927

sin (θ) = 0.61927

θ = 0.66781 \dots + 2 πn, θ = π - 0.66781 \dots + 2 πn

Degrees

θ = 38.26284 \dots^{\circ} + 36 0^{\circ} n, θ = 141.73715 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (θ) = 0.61927

Apply trig inverse properties

sin (θ) = 0.61927

General solutions for

sin (θ) = 0.61927

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

θ = arcsin (0.61927) + 2 πn, θ = π - arcsin (0.61927) + 2 πn

θ = arcsin (0.61927) + 2 πn, θ = π - arcsin (0.61927) + 2 πn

Show solutions in decimal form

θ = 0.66781 \dots + 2 πn, θ = π - 0.66781 \dots + 2 πn

sec (x) = \frac{- 2 3}{3}

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

6 sin^{2} (x) - sin (x) - 2 = 0

3 cos^{2} (x) - 8 cos (x) + 4 = 0, 0^{\circ} \leq x \leq 18 0^{\circ}

sin (x) = \frac{5}{25}

What is the general solution for sin(θ)=0.61927 ?
The general solution for sin(θ)=0.61927 is θ=0.66781…+2pin,θ=pi-0.66781…+2pin