What is the general solution for 0=2+4sin(θ) ?

The general solution for 0=2+4sin(θ) is θ=(7pi)/6+2pin,θ=(11pi)/6+2pin

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0=2+4sin(θ)

0 = 2 + 4 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

0 = 2 + 4 sin (θ)

Switch sides

2 + 4 sin (θ) = 0

Move

2

to the right side

2 + 4 sin (θ) = 0

Subtract

2

from both sides

2 + 4 sin (θ) - 2 = 0 - 2

Simplify

4 sin (θ) = - 2

4 sin (θ) = - 2

Divide both sides by

4

4 sin (θ) = - 2

Divide both sides by

4

\frac{4 sin ( θ )}{4} = \frac{- 2}{4}

Simplify

\frac{4 sin ( θ )}{4} = \frac{- 2}{4}

Simplify

\frac{4 sin ( θ )}{4} : sin (θ)

\frac{4 sin ( θ )}{4}

Divide the numbers:

\frac{4}{4} = 1

= sin (θ)

Simplify

\frac{- 2}{4} : - \frac{1}{2}

\frac{- 2}{4}

Apply the fraction rule:

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

= - \frac{2}{4}

Cancel the common factor:

2

= - \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{71}{81}

2 sin^{2} (2 x) - sin (2 x) - 3 = 0

cos (π + x) + cos (π + x) = 1

1 + 2 sin (θ) = 0

x, z = arcsin (x y)

What is the general solution for 0=2+4sin(θ) ?
The general solution for 0=2+4sin(θ) is θ=(7pi)/6+2pin,θ=(11pi)/6+2pin