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

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

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6sin(θ)=1

6 sin (θ) = 1

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

6 sin (θ) = 1

Divide both sides by

6

6 sin (θ) = 1

Divide both sides by

6

\frac{6 sin ( θ )}{6} = \frac{1}{6}

Simplify

sin (θ) = \frac{1}{6}

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

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