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

The general solution for 3sin^2(x)-sin(x)=0 is x=0.33983…+2pin,x=pi-0.33983…+2pin,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 >

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

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

x = 0.33983 \dots + 2 πn, x = π - 0.33983 \dots + 2 πn, x = 2 πn, x = π + 2 πn

Solution steps

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

Solve by substitution

sin (x) = \frac{1}{3}, sin (x) = 0

sin (x) = \frac{1}{3} : x = arcsin (\frac{1}{3}) + 2 πn, x = π - arcsin (\frac{1}{3}) + 2 πn

sin (x) = 0 : x = 2 πn, x = π + 2 πn

Combine all the solutions

x = arcsin (\frac{1}{3}) + 2 πn, x = π - arcsin (\frac{1}{3}) + 2 πn, x = 2 πn, x = π + 2 πn

Show solutions in decimal form

x = 0.33983 \dots + 2 πn, x = π - 0.33983 \dots + 2 πn, x = 2 πn, x = π + 2 πn

tan (x) = csc (x)

1 - csc^{2} (\frac{x}{2}) (\frac{1}{2}) = 0

0 = 1 - 2 sin (x)

3 csc (x) = 6

θ, x = sin (θ)

What is the general solution for 3sin^2(x)-sin(x)=0 ?
The general solution for 3sin^2(x)-sin(x)=0 is x=0.33983…+2pin,x=pi-0.33983…+2pin,x=2pin,x=pi+2pin