What is the general solution for sin(3x)=0,-2<x<2 ?

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

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sin(3x)=0,-2<x<2

sin (3 x) = 0, - 2 < x < 2

x = 0, x = \frac{π}{3}, x = - \frac{π}{3}

Degrees

x = 0^{\circ}, x = 6 0^{\circ}, x = - 6 0^{\circ}

Solution steps

sin (3 x) = 0, - 2 < x < 2

General solutions for

sin (3 x) = 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 = 0 + 2 πn, 3 x = π + 2 πn

3 x = 0 + 2 πn, 3 x = π + 2 πn

Solve

3 x = 0 + 2 πn : x = \frac{2 πn}{3}

3 x = 0 + 2 πn

0 + 2 πn = 2 πn

3 x = 2 πn

Divide both sides by

3

3 x = 2 πn

Divide both sides by

3

\frac{3 x}{3} = \frac{2 πn}{3}

Simplify

x = \frac{2 πn}{3}

x = \frac{2 πn}{3}

Solve

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

3 x = π + 2 πn

Divide both sides by

3

3 x = π + 2 πn

Divide both sides by

3

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

Simplify

x = \frac{π}{3} + \frac{2 πn}{3}

x = \frac{π}{3} + \frac{2 πn}{3}

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

Solutions for the range

- 2 < x < 2

x = 0, x = \frac{π}{3}, x = - \frac{π}{3}

tan (x) = \frac{2}{6}

2 sin^{2} (x) - 5 sin (x) = 3

cos (8 x) - cos (2 x) = sin (5 x)

tan (x) = - \frac{1}{5}

2 + 2 cos (x) = 0

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