What is the general solution for cos(28pi+x)= 1/2 ?

The general solution for cos(28pi+x)= 1/2 is x= pi/3+2pin-28pi,x=(5pi)/3+2pin-28pi

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cos(28pi+x)= 1/2

cos (28 π + x) = \frac{1}{2}

x = \frac{π}{3} + 2 πn - 28 π, x = \frac{5 π}{3} + 2 πn - 28 π

Degrees

x = - 498 0^{\circ} + 36 0^{\circ} n, x = - 474 0^{\circ} + 36 0^{\circ} n

Solution steps

cos (28 π + x) = \frac{1}{2}

General solutions for

cos (28 π + x) = \frac{1}{2}

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}

28 π + x = \frac{π}{3} + 2 πn, 28 π + x = \frac{5 π}{3} + 2 πn

28 π + x = \frac{π}{3} + 2 πn, 28 π + x = \frac{5 π}{3} + 2 πn

Solve

28 π + x = \frac{π}{3} + 2 πn : x = \frac{π}{3} + 2 πn - 28 π

28 π + x = \frac{π}{3} + 2 πn

Move

28 π

to the right side

28 π + x = \frac{π}{3} + 2 πn

Subtract

28 π

from both sides

28 π + x - 28 π = \frac{π}{3} + 2 πn - 28 π

Simplify

x = \frac{π}{3} + 2 πn - 28 π

x = \frac{π}{3} + 2 πn - 28 π