What is the general solution for sin(θ/2)=sqrt(2)-sin(θ/2) ?

The general solution for sin(θ/2)=sqrt(2)-sin(θ/2) is θ= pi/2+4pin,θ=(3pi)/2+4pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin(θ/2)=sqrt(2)-sin(θ/2)

sin (\frac{θ}{2}) = 2 - sin (\frac{θ}{2})

θ = \frac{π}{2} + 4 πn, θ = \frac{3 π}{2} + 4 πn

Solution steps

sin (\frac{θ}{2}) = 2 - sin (\frac{θ}{2})

Solve by substitution

sin (\frac{θ}{2}) = \frac{2}{2}

sin (\frac{θ}{2}) = \frac{2}{2} : θ = \frac{π}{2} + 4 πn, θ = \frac{3 π}{2} + 4 πn

Combine all the solutions

θ = \frac{π}{2} + 4 πn, θ = \frac{3 π}{2} + 4 πn

2 sin (x) cos (x) = cos (2 x)

(tan (x) + 1) (2 sin (x) - 1) = 0

sin (θ) = \frac{0.3924}{cos ( θ )}

x, y = 3 sin (x)

6 - 4 cos^{2} (x) - 5 cos (x) = 0

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