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

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

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

sin (3 x) = 0, 0 < x \leq 2

x = \frac{π}{3}

Degrees

x = 6 0^{\circ}

Solution steps

sin (3 x) = 0, 0 < x \leq 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

0 < x \leq 2

x = \frac{π}{3}

tan (x) = - 0.35

0 = cos (2 t - \frac{π}{3})

sin (0.5 x) = 0

cos (2 x) = 2 - 3 sin (x), \frac{π}{2} \leq x \leq \frac{3 π}{2}

3 sin (x) cos (x) = 0

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