What is the general solution for sin(θ)= 2/6 ?

The general solution for sin(θ)= 2/6 is θ=0.33983…+2pin,θ=pi-0.33983…+2pin

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sin(θ)= 2/6

sin (θ) = \frac{2}{6}

θ = 0.33983 \dots + 2 πn, θ = π - 0.33983 \dots + 2 πn

Degrees

θ = 19.47122 \dots^{\circ} + 36 0^{\circ} n, θ = 160.52877 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (θ) = \frac{2}{6}

Cancel the common factor:

2

sin (θ) = \frac{1}{3}

Apply trig inverse properties

sin (θ) = \frac{1}{3}

General solutions for

sin (θ) = \frac{1}{3}

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

θ = arcsin (\frac{1}{3}) + 2 πn, θ = π - arcsin (\frac{1}{3}) + 2 πn

θ = arcsin (\frac{1}{3}) + 2 πn, θ = π - arcsin (\frac{1}{3}) + 2 πn

Show solutions in decimal form

θ = 0.33983 \dots + 2 πn, θ = π - 0.33983 \dots + 2 πn

3 sin (2 x) = - 2

x, arctan (y) = 2 arctan (x)

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

tan (x) = \frac{7.3}{6.8}

cot (θ) = \frac{13}{6}

What is the general solution for sin(θ)= 2/6 ?
The general solution for sin(θ)= 2/6 is θ=0.33983…+2pin,θ=pi-0.33983…+2pin