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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

3 cos (θ) + 2 = 0

- cot (x) - 3 cos (x) = - cot (x) cos (x) - 3 cos (x)

6 cos^{2} (x) + 3 cos (x) = 0

6 sin (A) + 4 = 2 sin (A) + 8

(cot (x) - 3) (2 sin (x) + 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