What is the general solution for 8sin(θ)+4sqrt(3)=0 ?

The general solution for 8sin(θ)+4sqrt(3)=0 is θ=(4pi)/3+2pin,θ=(5pi)/3+2pin

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8sin(θ)+4sqrt(3)=0

8 sin (θ) + 43 = 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

8 sin (θ) + 43 = 0

Move

43

to the right side

8 sin (θ) + 43 = 0

Subtract

43

from both sides

8 sin (θ) + 43 - 43 = 0 - 43

Simplify

8 sin (θ) = - 43

8 sin (θ) = - 43

Divide both sides by

8

8 sin (θ) = - 43

Divide both sides by

8

\frac{8 sin ( θ )}{8} = \frac{- 4 3}{8}

Simplify

\frac{8 sin ( θ )}{8} = \frac{- 4 3}{8}

Simplify

\frac{8 sin ( θ )}{8} : sin (θ)

\frac{8 sin ( θ )}{8}

Divide the numbers:

\frac{8}{8} = 1

= sin (θ)

Simplify

\frac{- 4 3}{8} : - \frac{3}{2}

\frac{- 4 3}{8}

Apply the fraction rule:

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

= - \frac{4 3}{8}

Cancel the common factor:

4

= - \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

x, sin (x) = \frac{3}{2}

tan (α) = 2

sin (2 x + \frac{π}{4}) = \frac{2}{2}

cot (θ) = \frac{2}{3}

sec (θ) = \frac{6}{5}

What is the general solution for 8sin(θ)+4sqrt(3)=0 ?
The general solution for 8sin(θ)+4sqrt(3)=0 is θ=(4pi)/3+2pin,θ=(5pi)/3+2pin