What is the general solution for 0=sin(θ/2)-sin(θ) ?

The general solution for 0=sin(θ/2)-sin(θ) is θ=(2pi)/3+(8pin)/3 ,θ=2pi+(8pin)/3 ,θ=8pin,θ=4pi+8pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

0=sin(θ/2)-sin(θ)

0 = sin (\frac{θ}{2}) - sin (θ)

θ = \frac{2 π}{3} + \frac{8 πn}{3}, θ = 2 π + \frac{8 πn}{3}, θ = 8 πn, θ = 4 π + 8 πn

Solution steps

0 = sin (\frac{θ}{2}) - sin (θ)

Switch sides

sin (\frac{θ}{2}) - sin (θ) = 0

Rewrite using trig identities

- 2 cos (\frac{3 θ}{4}) sin (\frac{θ}{4}) = 0

Solving each part separately

cos (\frac{3 θ}{4}) = 0 or sin (\frac{θ}{4}) = 0

cos (\frac{3 θ}{4}) = 0 : θ = \frac{2 π}{3} + \frac{8 πn}{3}, θ = 2 π + \frac{8 πn}{3}

sin (\frac{θ}{4}) = 0 : θ = 8 πn, θ = 4 π + 8 πn

Combine all the solutions

θ = \frac{2 π}{3} + \frac{8 πn}{3}, θ = 2 π + \frac{8 πn}{3}, θ = 8 πn, θ = 4 π + 8 πn

sin (b) = 0.823

\frac{29}{sin ( 5 0 ^{\circ} )} = \frac{37}{sin ( x )}

arccos (θ) = 1.6

sin (9 0^{\circ} - θ) = 0.5745

sin (x) = \frac{60}{61}

What is the general solution for 0=sin(θ/2)-sin(θ) ?
The general solution for 0=sin(θ/2)-sin(θ) is θ=(2pi)/3+(8pin)/3 ,θ=2pi+(8pin)/3 ,θ=8pin,θ=4pi+8pin