What is the general solution for sin(-x)=sin(x) ?

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

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sin(-x)=sin(x)

sin (- x) = sin (x)

x = 2 πn, x = π + 2 πn

Degrees

x = 0^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n

Solution steps

sin (- x) = sin (x)

Rewrite using trig identities

sin (- x) = sin (x)

- sin (x) = sin (x)

- sin (x) = sin (x)

Subtract

sin (x)

from both sides

- 2 sin (x) = 0

Divide both sides by

- 2

- 2 sin (x) = 0

Divide both sides by

- 2

\frac{- 2 sin ( x )}{- 2} = \frac{0}{- 2}

Simplify

sin (x) = 0

sin (x) = 0

General solutions for

sin (x) = 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 = 0 + 2 πn, x = π + 2 πn

x = 0 + 2 πn, x = π + 2 πn

Solve

x = 0 + 2 πn : x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 2 πn, x = π + 2 πn

sin (x) = a

sin (6 x) - sin (2 x) = 0

z, cos (x) + cos (y) + cos (z) = 0

12 sin^{2} (x) + cos (x) - 6 = 0

2 sin (2 θ) - 1 = 0

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