What is the general solution for sin(θ)=0.422 ?

The general solution for sin(θ)=0.422 is θ=0.43565…+2pin,θ=pi-0.43565…+2pin

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sin(θ)=0.422

sin (θ) = 0.422

θ = 0.43565 \dots + 2 πn, θ = π - 0.43565 \dots + 2 πn

Degrees

θ = 24.96092 \dots^{\circ} + 36 0^{\circ} n, θ = 155.03907 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (θ) = 0.422

Apply trig inverse properties

sin (θ) = 0.422

General solutions for

sin (θ) = 0.422

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

θ = arcsin (0.422) + 2 πn, θ = π - arcsin (0.422) + 2 πn

θ = arcsin (0.422) + 2 πn, θ = π - arcsin (0.422) + 2 πn

Show solutions in decimal form

θ = 0.43565 \dots + 2 πn, θ = π - 0.43565 \dots + 2 πn

4 cos^{2} (x) + 3 cos (x) - 1 = 0

cos (x) = sin (x), 0 \leq x \leq 2 π

sin (4 (x - \frac{π}{4})) = 0

3 arcsin (2 θ) = 2 π

cos^{3} (x) + cos^{2} (x) - cos (x) - 1 = 0

What is the general solution for sin(θ)=0.422 ?
The general solution for sin(θ)=0.422 is θ=0.43565…+2pin,θ=pi-0.43565…+2pin