What is the general solution for cos(x+pi/6)=-1 ?

The general solution for cos(x+pi/6)=-1 is x=pi+2pin-pi/6

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cos(x+pi/6)=-1

cos (x + \frac{π}{6}) = - 1

x = π + 2 πn - \frac{π}{6}

Degrees

x = 15 0^{\circ} + 36 0^{\circ} n

Solution steps

cos (x + \frac{π}{6}) = - 1

General solutions for

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

x + \frac{π}{6} = π + 2 πn

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

Subtract

\frac{π}{6}

from 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 = π + 2 πn - \frac{π}{6}

tan (4 x + 20) \cdot cot (x + 5 0^{\circ}) = 1

csc (x) = - 0.5

cos (θ) - 4 = - 3

csc^{2} (x) + 2 csc (x) - 3 = - 4

- cos (θ) = 0

What is the general solution for cos(x+pi/6)=-1 ?
The general solution for cos(x+pi/6)=-1 is x=pi+2pin-pi/6