What is the general solution for 6sin(θ)+3=0 ?

The general solution for 6sin(θ)+3=0 is θ=(7pi)/6+2pin,θ=(11pi)/6+2pin

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6sin(θ)+3=0

6 sin (θ) + 3 = 0

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

6 sin (θ) + 3 = 0

Move

3

to the right side

6 sin (θ) + 3 = 0

Subtract

3

from both sides

6 sin (θ) + 3 - 3 = 0 - 3

Simplify

6 sin (θ) = - 3

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

2 cos (x) + sin (2 x) = 0

sin (3 θ) = - \frac{1}{2}

sin (x) (2 + 2 cos (x)) = 0

sec^{2} (x) + 5 tan (x) = 7

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

What is the general solution for 6sin(θ)+3=0 ?
The general solution for 6sin(θ)+3=0 is θ=(7pi)/6+2pin,θ=(11pi)/6+2pin