What is the general solution for sin(3x)+sin(2x)=0 ?

The general solution for sin(3x)+sin(2x)=0 is x=pi+4pin,x=3pi+4pin,x=(4pin)/5 ,x=(2pi)/5+(4pin)/5

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin(3x)+sin(2x)=0

sin (3 x) + sin (2 x) = 0

x = π + 4 πn, x = 3 π + 4 πn, x = \frac{4 πn}{5}, x = \frac{2 π}{5} + \frac{4 πn}{5}

Solution steps

sin (3 x) + sin (2 x) = 0

Rewrite using trig identities

2 cos (\frac{x}{2}) sin (\frac{5 x}{2}) = 0

Solving each part separately

cos (\frac{x}{2}) = 0 or sin (\frac{5 x}{2}) = 0

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

sin (\frac{5 x}{2}) = 0 : x = \frac{4 πn}{5}, x = \frac{2 π}{5} + \frac{4 πn}{5}

Combine all the solutions

x = π + 4 πn, x = 3 π + 4 πn, x = \frac{4 πn}{5}, x = \frac{2 π}{5} + \frac{4 πn}{5}

csc^{2} (x) + cot^{2} (x) = 3

csc^{2} (x) + cot^{2} (x) = 2

cos (x) = 0.24

\frac{π}{2} = sin (x)

sec^{4} (x) - 4 = 0

What is the general solution for sin(3x)+sin(2x)=0 ?
The general solution for sin(3x)+sin(2x)=0 is x=pi+4pin,x=3pi+4pin,x=(4pin)/5 ,x=(2pi)/5+(4pin)/5