What is the general solution for 2sin^2(x)=3sin(x)-1 ?

The general solution for 2sin^2(x)=3sin(x)-1 is x= pi/2+2pin,x= pi/6+2pin,x=(5pi)/6+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

2sin^2(x)=3sin(x)-1

2 sin^{2} (x) = 3 sin (x) - 1

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

Solution steps

2 sin^{2} (x) = 3 sin (x) - 1

Solve by substitution

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

sin (x) = 1 : x = \frac{π}{2} + 2 πn

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

Combine all the solutions

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

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

sin (4 x) + 1 = cos (4 x)

tan (x) = \frac{36}{28}

tan (x) = - 2 sin (x)

2 cos (θ) = 1

What is the general solution for 2sin^2(x)=3sin(x)-1 ?
The general solution for 2sin^2(x)=3sin(x)-1 is x= pi/2+2pin,x= pi/6+2pin,x=(5pi)/6+2pin