What is the general solution for sin(θ)= 4/7 ?

The general solution for sin(θ)= 4/7 is θ=0.60824…+2pin,θ=pi-0.60824…+2pin

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sin(θ)= 4/7

sin (θ) = \frac{4}{7}

θ = 0.60824 \dots + 2 πn, θ = π - 0.60824 \dots + 2 πn

Degrees

θ = 34.84990 \dots^{\circ} + 36 0^{\circ} n, θ = 145.15009 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (θ) = \frac{4}{7}

Apply trig inverse properties

sin (θ) = \frac{4}{7}

General solutions for

sin (θ) = \frac{4}{7}

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

θ = arcsin (\frac{4}{7}) + 2 πn, θ = π - arcsin (\frac{4}{7}) + 2 πn

θ = arcsin (\frac{4}{7}) + 2 πn, θ = π - arcsin (\frac{4}{7}) + 2 πn

Show solutions in decimal form

θ = 0.60824 \dots + 2 πn, θ = π - 0.60824 \dots + 2 πn

sin^{2} (θ) + 3 sin (θ) - 4 = 0

cos (2 θ) = \frac{2}{2}

4 cos (x) = 0

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

9 sin (2 x) sin (x) = 9 cos (x)

What is the general solution for sin(θ)= 4/7 ?
The general solution for sin(θ)= 4/7 is θ=0.60824…+2pin,θ=pi-0.60824…+2pin