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

The general solution for sin(x/6)=0 is x=12pin,x=6pi+12pin

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sin(x/6)=0

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

x = 12 πn, x = 6 π + 12 πn

Degrees

x = 0^{\circ} + 216 0^{\circ} n, x = 108 0^{\circ} + 216 0^{\circ} n

Solution steps

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

General solutions for

sin (\frac{x}{6}) = 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}

\frac{x}{6} = 0 + 2 πn, \frac{x}{6} = π + 2 πn

\frac{x}{6} = 0 + 2 πn, \frac{x}{6} = π + 2 πn

Solve

\frac{x}{6} = 0 + 2 πn : x = 12 πn

\frac{x}{6} = 0 + 2 πn

0 + 2 πn = 2 πn

\frac{x}{6} = 2 πn

Multiply both sides by

6

\frac{x}{6} = 2 πn

Multiply both sides by

6

\frac{6 x}{6} = 6 \cdot 2 πn

Simplify

x = 12 πn

x = 12 πn

Solve

\frac{x}{6} = π + 2 πn : x = 6 π + 12 πn

\frac{x}{6} = π + 2 πn

Multiply both sides by

6

\frac{x}{6} = π + 2 πn

Multiply both sides by

6

\frac{6 x}{6} = 6 π + 6 \cdot 2 πn

Simplify

x = 6 π + 12 πn

x = 6 π + 12 πn

x = 12 πn, x = 6 π + 12 πn

(tan (θ) - 1) (sec (θ) - 1) = 0, 0 \leq θ \leq 2 π

cos (θ) = \frac{4.4}{11}

x, cos^{3} (x) - cos (x) = 0

- 6 sin^{2} (θ) - 3 = sin (θ) - 5

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

What is the general solution for sin(x/6)=0 ?
The general solution for sin(x/6)=0 is x=12pin,x=6pi+12pin