What is the general solution for solvefor x,-sin(x+y)=0 ?

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

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solvefor x,-sin(x+y)=0

solve for

x, - sin (x + y) = 0

x = 2 πn - y, x = π + 2 πn - y

Solution steps

- sin (x + y) = 0

Divide both sides by

- 1

- sin (x + y) = 0

Divide both sides by

- 1

\frac{- sin ( x + y )}{- 1} = \frac{0}{- 1}

Simplify

sin (x + y) = 0

sin (x + y) = 0

General solutions for

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

x + y = 0 + 2 πn, x + y = π + 2 πn

Solve

x + y = 0 + 2 πn : x = 2 πn - y

x + y = 0 + 2 πn

0 + 2 πn = 2 πn

x + y = 2 πn

Move

y

to the right side

x + y = 2 πn

Subtract

y

from both sides

x + y - y = 2 πn - y

Simplify

x = 2 πn - y

x = 2 πn - y

Solve

x + y = π + 2 πn : x = π + 2 πn - y

x + y = π + 2 πn

Move

y

to the right side

x + y = π + 2 πn

Subtract

y

from both sides

x + y - y = π + 2 πn - y

Simplify

x = π + 2 πn - y

x = π + 2 πn - y

x = 2 πn - y, x = π + 2 πn - y

cot (θ) = - \frac{1}{2}

sin (2 θ) + sin (θ) + 2 cos (θ) + 1 = 0, 0 \leq θ \leq 2 π

sin^{2} (t) = cos^{2} (t)

cos (x) - sin (x) sin (2 x) = 0

4 sin (x) + 3 cos (x) = 4

What is the general solution for solvefor x,-sin(x+y)=0 ?
The general solution for solvefor x,-sin(x+y)=0 is x=2pin-y,x=pi+2pin-y