What is the general solution for sin(θ)= 40/60 ?

The general solution for sin(θ)= 40/60 is θ=0.72972…+2pin,θ=pi-0.72972…+2pin

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sin(θ)= 40/60

sin (θ) = \frac{40}{60}

θ = 0.72972 \dots + 2 πn, θ = π - 0.72972 \dots + 2 πn

Degrees

θ = 41.81031 \dots^{\circ} + 36 0^{\circ} n, θ = 138.18968 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (θ) = \frac{40}{60}

Cancel the common factor:

20

sin (θ) = \frac{2}{3}

Apply trig inverse properties

sin (θ) = \frac{2}{3}

General solutions for

sin (θ) = \frac{2}{3}

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

θ = arcsin (\frac{2}{3}) + 2 πn, θ = π - arcsin (\frac{2}{3}) + 2 πn

θ = arcsin (\frac{2}{3}) + 2 πn, θ = π - arcsin (\frac{2}{3}) + 2 πn

Show solutions in decimal form

θ = 0.72972 \dots + 2 πn, θ = π - 0.72972 \dots + 2 πn

10 = 3.44 sin (0.51 t + 4.11) + 9.48

2 cot^{2} (z) + 5 = 7 csc (z)

sin^{2} (x) = 6

sin^{2} (φ) + cos^{2} (φ) = 2

x, y^{2} (2 + sin (x)) = 1

What is the general solution for sin(θ)= 40/60 ?
The general solution for sin(θ)= 40/60 is θ=0.72972…+2pin,θ=pi-0.72972…+2pin