What is the general solution for 4sin(θ)+2sqrt(3)=0 ?

The general solution for 4sin(θ)+2sqrt(3)=0 is θ=(4pi)/3+2pin,θ=(5pi)/3+2pin

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4sin(θ)+2sqrt(3)=0

4 sin (θ) + 23 = 0

θ = \frac{4 π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn

Degrees

θ = 24 0^{\circ} + 36 0^{\circ} n, θ = 30 0^{\circ} + 36 0^{\circ} n

Solution steps

4 sin (θ) + 23 = 0

Move

23

to the right side

4 sin (θ) + 23 = 0

Subtract

23

from both sides

4 sin (θ) + 23 - 23 = 0 - 23

Simplify

4 sin (θ) = - 23

4 sin (θ) = - 23

Divide both sides by

4

4 sin (θ) = - 23

Divide both sides by

4

\frac{4 sin ( θ )}{4} = \frac{- 2 3}{4}

Simplify

\frac{4 sin ( θ )}{4} = \frac{- 2 3}{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 3}{4} : - \frac{3}{2}

\frac{- 2 3}{4}

Apply the fraction rule:

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

= - \frac{2 3}{4}

Cancel the common factor:

2

= - \frac{3}{2}

sin (θ) = - \frac{3}{2}

sin (θ) = - \frac{3}{2}

sin (θ) = - \frac{3}{2}

General solutions for

sin (θ) = - \frac{3}{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{4 π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn

θ = \frac{4 π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn

400 + 290 cos (x) + 290 sin (x) = 0

2 = 2 sin (2 θ)

4 sin^{2} (x) + 4 cos (x) - 5 = 0, (0, 2 π)

a, E = 25 (sin (a) - cos (a))

391 = 78 \cdot 21.5 \cdot cos (x)

What is the general solution for 4sin(θ)+2sqrt(3)=0 ?
The general solution for 4sin(θ)+2sqrt(3)=0 is θ=(4pi)/3+2pin,θ=(5pi)/3+2pin