What is the general solution for 0=sin(x+c) ?

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

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0=sin(x+c)

0 = sin (x + c)

x = 2 πn - c, x = π + 2 πn - c

Solution steps

0 = sin (x + c)

Switch sides

sin (x + c) = 0

General solutions for

sin (x + c) = 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 + c = 0 + 2 πn, x + c = π + 2 πn

x + c = 0 + 2 πn, x + c = π + 2 πn

Solve

x + c = 0 + 2 πn : x = 2 πn - c

x + c = 0 + 2 πn

0 + 2 πn = 2 πn

x + c = 2 πn

Move

c

to the right side

x + c = 2 πn

Subtract

c

from both sides

x + c - c = 2 πn - c

Simplify

x = 2 πn - c

x = 2 πn - c