What is the general solution for sin(2x)=5sin(x) ?

The general solution for sin(2x)=5sin(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(2x)=5sin(x)

sin (2 x) = 5 sin (x)

x = 2 πn, x = π + 2 πn

Solution steps

sin (2 x) = 5 sin (x)

Subtract

5 sin (x)

from both sides

sin (2 x) - 5 sin (x) = 0

Rewrite using trig identities

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

Factor

- 5 sin (x) + 2 cos (x) sin (x) : sin (x) (2 cos (x) - 5)

sin (x) (2 cos (x) - 5) = 0

Solving each part separately

sin (x) = 0 or 2 cos (x) - 5 = 0

sin (x) = 0 : x = 2 πn, x = π + 2 πn

2 cos (x) - 5 = 0 :

No Solution

Combine all the solutions

x = 2 πn, x = π + 2 πn

2 cos^{2} (θ) - 4 cos (θ) - 1 = - 5 cos (θ)

- 2 sin^{2} (x) - sin (x) + 3 = 0

tan (x) = - 3 + 2

3 tan (x) - cot (x) = 0

sin^{2} (x) = \frac{( 2 m - 1 )}{4}

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