What is the general solution for 4sin(x-pi)+2=0 ?

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

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4sin(x-pi)+2=0

Solution

4 sin (x - π) + 2 = 0

Solution

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

Degrees

x = 39 0^{\circ} + 36 0^{\circ} n, x = 51 0^{\circ} + 36 0^{\circ} n

Solution steps

4 sin (x - π) + 2 = 0

Move

2

to the right side

4 sin (x - π) + 2 = 0

Subtract

2

from both sides

4 sin (x - π) + 2 - 2 = 0 - 2

Simplify

4 sin (x - π) = - 2

4 sin (x - π) = - 2

Divide both sides by

4

4 sin (x - π) = - 2

Divide both sides by

4

\frac{4 sin ( x - π )}{4} = \frac{- 2}{4}

Simplify

\frac{4 sin ( x - π )}{4} = \frac{- 2}{4}

Simplify

\frac{4 sin ( x - π )}{4} : sin (x - π)

\frac{4 sin ( x - π )}{4}

Divide the numbers:

\frac{4}{4} = 1

= sin (x - π)

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 (x - π) = - \frac{1}{2}

sin (x - π) = - \frac{1}{2}

sin (x - π) = - \frac{1}{2}

General solutions for

sin (x - π) = - \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}

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

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

Solve

x - π = \frac{7 π}{6} + 2 πn : x = \frac{7 π}{6} + 2 πn + π

x - π = \frac{7 π}{6} + 2 πn

Move

π

to the right side

x - π = \frac{7 π}{6} + 2 πn

Add

π

to both sides

x - π + π = \frac{7 π}{6} + 2 πn + π

Simplify

x = \frac{7 π}{6} + 2 πn + π

x = \frac{7 π}{6} + 2 πn + π

Solve

x - π = \frac{11 π}{6} + 2 πn : x = \frac{11 π}{6} + 2 πn + π

x - π = \frac{11 π}{6} + 2 πn

Move

π

to the right side

x - π = \frac{11 π}{6} + 2 πn

Add

π

to both sides

x - π + π = \frac{11 π}{6} + 2 πn + π

Simplify

x = \frac{11 π}{6} + 2 πn + π

x = \frac{11 π}{6} + 2 πn + π

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

Graph

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Frequently Asked Questions (FAQ)

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