What is the general solution for sin(x+5pi)=0 ?

The general solution for sin(x+5pi)=0 is x=2pin-5pi,x=-4pi+2pin

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sin(x+5pi)=0

sin (x + 5 π) = 0

x = 2 πn - 5 π, x = - 4 π + 2 πn

Degrees

x = - 90 0^{\circ} + 36 0^{\circ} n, x = - 72 0^{\circ} + 36 0^{\circ} n

Solution steps

sin (x + 5 π) = 0

General solutions for

sin (x + 5 π) = 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 + 5 π = 0 + 2 πn, x + 5 π = π + 2 πn

x + 5 π = 0 + 2 πn, x + 5 π = π + 2 πn

Solve

x + 5 π = 0 + 2 πn : x = 2 πn - 5 π

x + 5 π = 0 + 2 πn

0 + 2 πn = 2 πn

x + 5 π = 2 πn

Move

5 π

to the right side

x + 5 π = 2 πn

Subtract

5 π

from both sides

x + 5 π - 5 π = 2 πn - 5 π

Simplify

x = 2 πn - 5 π

x = 2 πn - 5 π