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

The general solution for -sin(x)+2sin(2x)=0 is x=2pin,x=pi+2pin,x=1.31811…+2pin,x=2pi-1.31811…+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

x = 2 πn, x = π + 2 πn, x = 1.31811 \dots + 2 πn, x = 2 π - 1.31811 \dots + 2 πn

Solution steps

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

Rewrite using trig identities

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

Factor

- sin (x) + 4 cos (x) sin (x) : sin (x) (4 cos (x) - 1)

sin (x) (4 cos (x) - 1) = 0

Solving each part separately

sin (x) = 0 or 4 cos (x) - 1 = 0

sin (x) = 0 : x = 2 πn, x = π + 2 πn

4 cos (x) - 1 = 0 : x = arccos (\frac{1}{4}) + 2 πn, x = 2 π - arccos (\frac{1}{4}) + 2 πn

Combine all the solutions

x = 2 πn, x = π + 2 πn, x = arccos (\frac{1}{4}) + 2 πn, x = 2 π - arccos (\frac{1}{4}) + 2 πn

Show solutions in decimal form

x = 2 πn, x = π + 2 πn, x = 1.31811 \dots + 2 πn, x = 2 π - 1.31811 \dots + 2 πn

arccos (x) = arcsin (\frac{3}{5})

x, y = 2 tan (x)

sin^{2} (x) - cos^{2} (x) - 1 = 0

tan (x) - 1 = - \frac{1}{3} + \frac{1}{3} cot (x)

tan^{2} (x) - 3 tan (x) = 0, 0 \leq x \leq 2 π

What is the general solution for -sin(x)+2sin(2x)=0 ?
The general solution for -sin(x)+2sin(2x)=0 is x=2pin,x=pi+2pin,x=1.31811…+2pin,x=2pi-1.31811…+2pin