What is the general solution for -6sin(θ)=-3sqrt(2) ?

The general solution for -6sin(θ)=-3sqrt(2) is θ= pi/4+2pin,θ=(3pi)/4+2pin

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-6sin(θ)=-3sqrt(2)

- 6 sin (θ) = - 32

θ = \frac{π}{4} + 2 πn, θ = \frac{3 π}{4} + 2 πn

Degrees

θ = 4 5^{\circ} + 36 0^{\circ} n, θ = 13 5^{\circ} + 36 0^{\circ} n

Solution steps

- 6 sin (θ) = - 32

Divide both sides by

- 6

- 6 sin (θ) = - 32

Divide both sides by

- 6

\frac{- 6 sin ( θ )}{- 6} = \frac{- 3 2}{- 6}

Simplify

\frac{- 6 sin ( θ )}{- 6} = \frac{- 3 2}{- 6}

Simplify

\frac{- 6 sin ( θ )}{- 6} : sin (θ)

\frac{- 6 sin ( θ )}{- 6}

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

= \frac{6 sin ( θ )}{6}

Divide the numbers:

\frac{6}{6} = 1

= sin (θ)

Simplify

\frac{- 3 2}{- 6} : \frac{2}{2}

\frac{- 3 2}{- 6}

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

= \frac{3 2}{6}

Cancel the common factor:

3

= \frac{2}{2}

sin (θ) = \frac{2}{2}

sin (θ) = \frac{2}{2}

sin (θ) = \frac{2}{2}

General solutions for

sin (θ) = \frac{2}{2}

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

θ = \frac{π}{4} + 2 πn, θ = \frac{3 π}{4} + 2 πn

θ = \frac{π}{4} + 2 πn, θ = \frac{3 π}{4} + 2 πn

cos (x) = \frac{4 ( \frac{1}{2} ) - 1}{3}

sin (x) = \frac{π}{4} + \frac{0 π}{2}

cos (2 x) - sin (x) - 1 = 0

cos (x) = \frac{5}{20}

cos^{2} (x) + sin^{2} (x) = 2

What is the general solution for -6sin(θ)=-3sqrt(2) ?
The general solution for -6sin(θ)=-3sqrt(2) is θ= pi/4+2pin,θ=(3pi)/4+2pin