What is the general solution for sin(x)+sin(2x)=0 ?

The general solution for sin(x)+sin(2x)=0 is x=2pin,x=pi+2pin,x=(2pi)/3+2pin,x=(4pi)/3+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin(x)+sin(2x)=0

sin (x) + sin (2 x) = 0

x = 2 πn, x = π + 2 πn, x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

Solution steps

sin (x) + sin (2 x) = 0

Rewrite using trig identities

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

Factor

sin (x) + 2 cos (x) sin (x) : sin (x) (2 cos (x) + 1)

sin (x) (2 cos (x) + 1) = 0

Solving each part separately

sin (x) = 0 or 2 cos (x) + 1 = 0

sin (x) = 0 : x = 2 πn, x = π + 2 πn

2 cos (x) + 1 = 0 : x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

Combine all the solutions

x = 2 πn, x = π + 2 πn, x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

tan (θ) + 3 = 0

csc (\frac{π}{2})

2 cos (x) = 3

csc (3 0^{\circ})

2 sin^{2} (x) + sin (x) - 1 = 0

What is the general solution for sin(x)+sin(2x)=0 ?
The general solution for sin(x)+sin(2x)=0 is x=2pin,x=pi+2pin,x=(2pi)/3+2pin,x=(4pi)/3+2pin