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

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

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sin(x-pi/6)=0

sin (x - \frac{π}{6}) = 0

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

Degrees

x = 3 0^{\circ} + 36 0^{\circ} n, x = 21 0^{\circ} + 36 0^{\circ} n

Solution steps

sin (x - \frac{π}{6}) = 0

General solutions for

sin (x - \frac{π}{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}

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

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

Solve

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

x - \frac{π}{6} = 0 + 2 πn

0 + 2 πn = 2 πn

x - \frac{π}{6} = 2 πn

Move

\frac{π}{6}

to the right side

x - \frac{π}{6} = 2 πn

Add

\frac{π}{6}

to both sides

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

Simplify

x = 2 πn + \frac{π}{6}

x = 2 πn + \frac{π}{6}

Solve

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

x - \frac{π}{6} = π + 2 πn

Move

\frac{π}{6}

to the right side

x - \frac{π}{6} = π + 2 πn

Add

\frac{π}{6}

to both sides

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

Simplify

x = π + 2 πn + \frac{π}{6}

x = π + 2 πn + \frac{π}{6}

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

2 = \frac{1}{cos ^{2} ( x )}

arccot (x - 2) = arccot (x - 1) + arccot (x)

tan (x) - \frac{2}{tan ( x )} = 1

sin (x) + 3 cos (x) = 2

arccos (2 x) = π

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