What is the general solution for -5sin(3x-pi)=0 ?

The general solution for -5sin(3x-pi)=0 is x=(2pin)/3+pi/3 ,x=(2pi)/3+(2pin)/3

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Popular Trigonometry >

-5sin(3x-pi)=0

Solution

- 5 sin (3 x - π) = 0

Solution

x = \frac{2 πn}{3} + \frac{π}{3}, x = \frac{2 π}{3} + \frac{2 πn}{3}

Degrees

x = 6 0^{\circ} + 12 0^{\circ} n, x = 12 0^{\circ} + 12 0^{\circ} n

Solution steps

- 5 sin (3 x - π) = 0

Divide both sides by

- 5

- 5 sin (3 x - π) = 0

Divide both sides by

- 5

\frac{- 5 sin ( 3 x - π )}{- 5} = \frac{0}{- 5}

Simplify

sin (3 x - π) = 0

sin (3 x - π) = 0

General solutions for

sin (3 x - π) = 0

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}

3 x - π = 0 + 2 πn, 3 x - π = π + 2 πn

3 x - π = 0 + 2 πn, 3 x - π = π + 2 πn

Solve

3 x - π = 0 + 2 πn : x = \frac{2 πn}{3} + \frac{π}{3}

3 x - π = 0 + 2 πn

0 + 2 πn = 2 πn

3 x - π = 2 πn

Move

π

to the right side

3 x - π = 2 πn

Add

π

to both sides

3 x - π + π = 2 πn + π

Simplify

3 x = 2 πn + π

3 x = 2 πn + π

Divide both sides by

3

3 x = 2 πn + π

Divide both sides by

3

\frac{3 x}{3} = \frac{2 πn}{3} + \frac{π}{3}

Simplify

x = \frac{2 πn}{3} + \frac{π}{3}

x = \frac{2 πn}{3} + \frac{π}{3}

Solve

3 x - π = π + 2 πn : x = \frac{2 π}{3} + \frac{2 πn}{3}

3 x - π = π + 2 πn

Move

π

to the right side

3 x - π = π + 2 πn

Add

π

to both sides

3 x - π + π = π + 2 πn + π

Simplify

3 x = 2 π + 2 πn

3 x = 2 π + 2 πn

Divide both sides by

3

3 x = 2 π + 2 πn

Divide both sides by

3

\frac{3 x}{3} = \frac{2 π}{3} + \frac{2 πn}{3}

Simplify

x = \frac{2 π}{3} + \frac{2 πn}{3}

x = \frac{2 π}{3} + \frac{2 πn}{3}

x = \frac{2 πn}{3} + \frac{π}{3}, x = \frac{2 π}{3} + \frac{2 πn}{3}

Graph

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Frequently Asked Questions (FAQ)

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