What is the general solution for 2sin(x/2)-1=0 ?

The general solution for 2sin(x/2)-1=0 is x= pi/3+4pin,x=(5pi)/3+4pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

2sin(x/2)-1=0

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

x = \frac{π}{3} + 4 πn, x = \frac{5 π}{3} + 4 πn

Solution steps

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

Move

1

to the right side

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

Divide both sides by

2

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

General solutions for

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

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

Solve

\frac{x}{2} = \frac{π}{6} + 2 πn : x = \frac{π}{3} + 4 πn

Solve

\frac{x}{2} = \frac{5 π}{6} + 2 πn : x = \frac{5 π}{3} + 4 πn

x = \frac{π}{3} + 4 πn, x = \frac{5 π}{3} + 4 πn

cot (\frac{θ}{7}) = 12

cos (x) sin (x) + sin (x) = 0

2 sin (θ) + 6 = 5

3 sin (θ) - 3 = sin (θ)

cos (x) = \frac{15}{17}

What is the general solution for 2sin(x/2)-1=0 ?
The general solution for 2sin(x/2)-1=0 is x= pi/3+4pin,x=(5pi)/3+4pin