What is the general solution for -36sin(6x)=0 ?

The general solution for -36sin(6x)=0 is x=(pin)/3 ,x= pi/6+(pin)/3

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-36sin(6x)=0

- 36 sin (6 x) = 0

x = \frac{πn}{3}, x = \frac{π}{6} + \frac{πn}{3}

Degrees

x = 0^{\circ} + 6 0^{\circ} n, x = 3 0^{\circ} + 6 0^{\circ} n

Solution steps

- 36 sin (6 x) = 0

Divide both sides by

- 36

- 36 sin (6 x) = 0

Divide both sides by

- 36

\frac{- 36 sin ( 6 x )}{- 36} = \frac{0}{- 36}

Simplify

sin (6 x) = 0

sin (6 x) = 0

General solutions for

sin (6 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}

6 x = 0 + 2 πn, 6 x = π + 2 πn

6 x = 0 + 2 πn, 6 x = π + 2 πn

Solve

6 x = 0 + 2 πn : x = \frac{πn}{3}

6 x = 0 + 2 πn

0 + 2 πn = 2 πn

6 x = 2 πn

Divide both sides by

6

6 x = 2 πn

Divide both sides by

6

\frac{6 x}{6} = \frac{2 πn}{6}

Simplify

x = \frac{πn}{3}

x = \frac{πn}{3}

Solve

6 x = π + 2 πn : x = \frac{π}{6} + \frac{πn}{3}

6 x = π + 2 πn

Divide both sides by

6

6 x = π + 2 πn

Divide both sides by

6

\frac{6 x}{6} = \frac{π}{6} + \frac{2 πn}{6}

Simplify

x = \frac{π}{6} + \frac{πn}{3}

x = \frac{π}{6} + \frac{πn}{3}

x = \frac{πn}{3}, x = \frac{π}{6} + \frac{πn}{3}

2 sin (x) cos (x) = tan (x)

2 cos^{2} (2 x) + sin (2 x) = 1

sin (4 θ) + sin (2 θ) = 0

sec (x) = \frac{2}{3}

2 sin (x) + 1 = 3 csc (x)

What is the general solution for -36sin(6x)=0 ?
The general solution for -36sin(6x)=0 is x=(pin)/3 ,x= pi/6+(pin)/3