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

The general solution for 2sin^2(x)=sin(x) is x= pi/6+2pin,x=(5pi)/6+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 >

2sin^2(x)=sin(x)

2 sin^{2} (x) = sin (x)

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn, x = 2 πn, x = π + 2 πn

Solution steps

2 sin^{2} (x) = sin (x)

Solve by substitution

sin (x) = \frac{1}{2}, sin (x) = 0

sin (x) = \frac{1}{2} : x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

sin (x) = 0 : x = 2 πn, x = π + 2 πn

Combine all the solutions

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn, x = 2 πn, x = π + 2 πn

arccos (\frac{1}{2})

sin (θ) sin (2 θ) = 0

sin (\frac{11 π}{6})

tan (\frac{11 π}{6})

2 sin (θ) - 3 = 0

What is the general solution for 2sin^2(x)=sin(x) ?
The general solution for 2sin^2(x)=sin(x) is x= pi/6+2pin,x=(5pi)/6+2pin,x=2pin,x=pi+2pin