What is the general solution for cos(x-pi/(13))=-1 ?

The general solution for cos(x-pi/(13))=-1 is x=pi+2pin+pi/(13)

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cos(x-pi/(13))=-1

cos (x - \frac{π}{13}) = - 1

x = π + 2 πn + \frac{π}{13}

Degrees

x = 193.84615 \dots^{\circ} + 36 0^{\circ} n

Solution steps

cos (x - \frac{π}{13}) = - 1

General solutions for

cos (x - \frac{π}{13}) = - 1

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

x - \frac{π}{13} = π + 2 πn

x - \frac{π}{13} = π + 2 πn

Solve

x - \frac{π}{13} = π + 2 πn : x = π + 2 πn + \frac{π}{13}

x - \frac{π}{13} = π + 2 πn

Move

\frac{π}{13}

to the right side

x - \frac{π}{13} = π + 2 πn

Add

\frac{π}{13}

to both sides

x - \frac{π}{13} + \frac{π}{13} = π + 2 πn + \frac{π}{13}

Simplify

x = π + 2 πn + \frac{π}{13}

x = π + 2 πn + \frac{π}{13}

x = π + 2 πn + \frac{π}{13}

What is the general solution for cos(x-pi/(13))=-1 ?
The general solution for cos(x-pi/(13))=-1 is x=pi+2pin+pi/(13)