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

The general solution for 3sin(2x)-sin(x)=0 is x=2pin,x=pi+2pin,x=1.40334…+2pin,x=2pi-1.40334…+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

x = 2 πn, x = π + 2 πn, x = 1.40334 \dots + 2 πn, x = 2 π - 1.40334 \dots + 2 πn

Solution steps

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

Rewrite using trig identities

- sin (x) + 6 cos (x) sin (x) = 0

Factor

- sin (x) + 6 cos (x) sin (x) : sin (x) (6 cos (x) - 1)

sin (x) (6 cos (x) - 1) = 0

Solving each part separately

sin (x) = 0 or 6 cos (x) - 1 = 0

sin (x) = 0 : x = 2 πn, x = π + 2 πn

6 cos (x) - 1 = 0 : x = arccos (\frac{1}{6}) + 2 πn, x = 2 π - arccos (\frac{1}{6}) + 2 πn

Combine all the solutions

x = 2 πn, x = π + 2 πn, x = arccos (\frac{1}{6}) + 2 πn, x = 2 π - arccos (\frac{1}{6}) + 2 πn

Show solutions in decimal form

x = 2 πn, x = π + 2 πn, x = 1.40334 \dots + 2 πn, x = 2 π - 1.40334 \dots + 2 πn

(- 6 cos (x) - 5 sin (x))^{2} + 11 sin^{2} (x) = 51

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

cosh (4 x) = 0

x, tan (2 x) = - \frac{( \frac{30 + 20}{2} )}{80}

4 cos (3 θ) = 2

What is the general solution for 3sin(2x)-sin(x)=0 ?
The general solution for 3sin(2x)-sin(x)=0 is x=2pin,x=pi+2pin,x=1.40334…+2pin,x=2pi-1.40334…+2pin