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

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

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sin(x/3)=0

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

x = 6 πn, x = 3 π + 6 πn

Degrees

x = 0^{\circ} + 108 0^{\circ} n, x = 54 0^{\circ} + 108 0^{\circ} n

Solution steps

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

General solutions for

sin (\frac{x}{3}) = 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}{3} = 0 + 2 πn, \frac{x}{3} = π + 2 πn

\frac{x}{3} = 0 + 2 πn, \frac{x}{3} = π + 2 πn

Solve

\frac{x}{3} = 0 + 2 πn : x = 6 πn

\frac{x}{3} = 0 + 2 πn

0 + 2 πn = 2 πn

\frac{x}{3} = 2 πn

Multiply both sides by

3

\frac{x}{3} = 2 πn

Multiply both sides by

3

\frac{3 x}{3} = 3 \cdot 2 πn

Simplify

x = 6 πn

x = 6 πn

Solve

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

\frac{x}{3} = π + 2 πn

Multiply both sides by

3

\frac{x}{3} = π + 2 πn

Multiply both sides by

3

\frac{3 x}{3} = 3 π + 3 \cdot 2 πn

Simplify

x = 3 π + 6 πn

x = 3 π + 6 πn

x = 6 πn, x = 3 π + 6 πn

cos (x) = 0.95

2 cos (2 θ) + 2 cos (θ) + 2 = 3 cos (θ)

1 + csc (x) = cot^{2} (x)

cos (\frac{1}{4 θ}) = \frac{- 2}{2}

cos (x) tan (x) - 2 cos^{2} (x) = - 1

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