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 = 189.59406 \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

cos (x) = 0.788

- 3 cos (x) = 2 sin^{2} (x)

3 cot^{2} (θ) = 1

tan (x) - 2 = 3

3 cos (x) - 2 = 0

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