What is the general solution for sin(θ)= 1/6 ?

The general solution for sin(θ)= 1/6 is θ=0.16744…+2pin,θ=pi-0.16744…+2pin

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sin(θ)= 1/6

sin (θ) = \frac{1}{6}

θ = 0.16744 \dots + 2 πn, θ = π - 0.16744 \dots + 2 πn

Degrees

θ = 9.59406 \dots^{\circ} + 36 0^{\circ} n, θ = 170.40593 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (θ) = \frac{1}{6}

Apply trig inverse properties

sin (θ) = \frac{1}{6}

General solutions for

sin (θ) = \frac{1}{6}

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

θ = arcsin (\frac{1}{6}) + 2 πn, θ = π - arcsin (\frac{1}{6}) + 2 πn

θ = arcsin (\frac{1}{6}) + 2 πn, θ = π - arcsin (\frac{1}{6}) + 2 πn

Show solutions in decimal form

θ = 0.16744 \dots + 2 πn, θ = π - 0.16744 \dots + 2 πn

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

sin (\frac{x}{4}) = 0

sin (\frac{4 π}{11}) = sin (θ) \cdot sin (\frac{7 π}{11})

sin (2 x) = 2 tan (2 x)

- 2 cos (2 θ) + 12 = 4 sin (θ) + 9

What is the general solution for sin(θ)= 1/6 ?
The general solution for sin(θ)= 1/6 is θ=0.16744…+2pin,θ=pi-0.16744…+2pin