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

The general solution for -3=6sin(θ) is θ=(7pi)/6+2pin,θ=(11pi)/6+2pin

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-3=6sin(θ)

- 3 = 6 sin (θ)

θ = \frac{7 π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

Degrees

θ = 21 0^{\circ} + 36 0^{\circ} n, θ = 33 0^{\circ} + 36 0^{\circ} n

Solution steps

- 3 = 6 sin (θ)

Switch sides

6 sin (θ) = - 3

Divide both sides by

6

6 sin (θ) = - 3

Divide both sides by

6

\frac{6 sin ( θ )}{6} = \frac{- 3}{6}

Simplify

\frac{6 sin ( θ )}{6} = \frac{- 3}{6}

Simplify

\frac{6 sin ( θ )}{6} : sin (θ)

\frac{6 sin ( θ )}{6}

Divide the numbers:

\frac{6}{6} = 1

= sin (θ)

Simplify

\frac{- 3}{6} : - \frac{1}{2}

\frac{- 3}{6}

Apply the fraction rule:

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

= - \frac{3}{6}

Cancel the common factor:

3

= - \frac{1}{2}

sin (θ) = - \frac{1}{2}

sin (θ) = - \frac{1}{2}

sin (θ) = - \frac{1}{2}

General solutions for

sin (θ) = - \frac{1}{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{7 π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

θ = \frac{7 π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

cos (x) = \frac{- 4}{5}

\frac{1}{cos ( θ )} + tan (θ) = 2

3 cot (\frac{3}{2}) + 2 csc (\frac{x}{2}) = 0, 0^{\circ} \leq, x \leq 36 0^{\circ}

cos (x) = 2 cos (4 5^{\circ} + x)

2 sin (θ) = 1.124

What is the general solution for -3=6sin(θ) ?
The general solution for -3=6sin(θ) is θ=(7pi)/6+2pin,θ=(11pi)/6+2pin