What is the general solution for -6sin(3x)=0 ?

The general solution for -6sin(3x)=0 is x=(2pin)/3 ,x= pi/3+(2pin)/3

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-6sin(3x)=0

- 6 sin (3 x) = 0

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

Degrees

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

Solution steps

- 6 sin (3 x) = 0

Divide both sides by

- 6

- 6 sin (3 x) = 0

Divide both sides by

- 6

\frac{- 6 sin ( 3 x )}{- 6} = \frac{0}{- 6}

Simplify

sin (3 x) = 0

sin (3 x) = 0

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}

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

2 tan (2 x) - 6 = 0

8 sin (θ) + 15 cos (θ) = 18

\frac{30}{sin ( A )} = \frac{34.4}{sin ( 6 2 ^{\circ} )}

- 2 sin (x) = 1

What is the general solution for -6sin(3x)=0 ?
The general solution for -6sin(3x)=0 is x=(2pin)/3 ,x= pi/3+(2pin)/3