What is the general solution for 2-3sin(θ)=0 ?

The general solution for 2-3sin(θ)=0 is θ=0.72972…+2pin,θ=pi-0.72972…+2pin

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2-3sin(θ)=0

2 - 3 sin (θ) = 0

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

2 - 3 sin (θ) = 0

Move

2

to the right side

2 - 3 sin (θ) = 0

Subtract

2

from both sides

2 - 3 sin (θ) - 2 = 0 - 2

Simplify

- 3 sin (θ) = - 2

- 3 sin (θ) = - 2

Divide both sides by

- 3

- 3 sin (θ) = - 2

Divide both sides by

- 3

\frac{- 3 sin ( θ )}{- 3} = \frac{- 2}{- 3}

Simplify

sin (θ) = \frac{2}{3}

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

cos (x) = - 0.83

y, x = cot (y)

x, 2 cos (\frac{π x}{3}) = 1

cos (x) = - 0.16

cos (x) = - 0.39

What is the general solution for 2-3sin(θ)=0 ?
The general solution for 2-3sin(θ)=0 is θ=0.72972…+2pin,θ=pi-0.72972…+2pin