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

The general solution for sin(x)sin(2x)=sin(3x) is x=2pin,x=pi+2pin,x= pi/4+pin,x=-1.24904…+pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin(x)sin(2x)=sin(3x)

sin (x) sin (2 x) = sin (3 x)

x = 2 πn, x = π + 2 πn, x = \frac{π}{4} + πn, x = - 1.24904 \dots + πn

Solution steps

sin (x) sin (2 x) = sin (3 x)

Subtract

sin (3 x)

from both sides

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

Rewrite using trig identities

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

Factor

sin^{3} (x) + sin (2 x) sin (x) - 3 cos^{2} (x) sin (x) : sin (x) (sin^{2} (x) + sin (2 x) - 3 cos^{2} (x))

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

Solving each part separately

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

sin (x) = 0 : x = 2 πn, x = π + 2 πn

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

Combine all the solutions

x = 2 πn, x = π + 2 πn, x = \frac{π}{4} + πn, x = arctan (- 3) + πn

Show solutions in decimal form

x = 2 πn, x = π + 2 πn, x = \frac{π}{4} + πn, x = - 1.24904 \dots + πn

cot (x) = \frac{15}{8}

cos (θ) = \frac{- 5}{4}

x, y = 5 cos (8 x) - y

csc (θ) = \frac{3}{2}, \frac{π}{2} < θ < \frac{3 π}{2}

tan (x) = \frac{5.1}{4.2}

What is the general solution for sin(x)sin(2x)=sin(3x) ?
The general solution for sin(x)sin(2x)=sin(3x) is x=2pin,x=pi+2pin,x= pi/4+pin,x=-1.24904…+pin