What is the general solution for sin(3x)=sin(5x) ?

The general solution for sin(3x)=sin(5x) is x= pi/8+(pin)/2 ,x=(3pi)/8+(pin)/2 ,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(3x)=sin(5x)

sin (3 x) = sin (5 x)

x = \frac{π}{8} + \frac{πn}{2}, x = \frac{3 π}{8} + \frac{πn}{2}, x = 2 πn, x = π + 2 πn

Solution steps

sin (3 x) = sin (5 x)

Subtract

sin (5 x)

from both sides

sin (3 x) - sin (5 x) = 0

Rewrite using trig identities

- 2 cos (4 x) sin (x) = 0

Solving each part separately

cos (4 x) = 0 or sin (x) = 0

cos (4 x) = 0 : x = \frac{π}{8} + \frac{πn}{2}, x = \frac{3 π}{8} + \frac{πn}{2}

sin (x) = 0 : x = 2 πn, x = π + 2 πn

Combine all the solutions

x = \frac{π}{8} + \frac{πn}{2}, x = \frac{3 π}{8} + \frac{πn}{2}, x = 2 πn, x = π + 2 πn

2 sin^{2} (3 θ) + sin (3 θ) - 1 = 0

4 cos (θ) + 3 = 2 cos (θ)

sin (2 x) = \frac{1}{2}, 0 \leq x < 2 π

6 cos^{2} (θ) - cos (θ) - 1 = 0

11 tan (x) + 6 = 3 tan (x) + 6

What is the general solution for sin(3x)=sin(5x) ?
The general solution for sin(3x)=sin(5x) is x= pi/8+(pin)/2 ,x=(3pi)/8+(pin)/2 ,x=2pin,x=pi+2pin