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

The general solution for 1/2-sin(x)=0 is 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 >

1/2-sin(x)=0

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

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

Degrees

x = 3 0^{\circ} + 36 0^{\circ} n, x = 15 0^{\circ} + 36 0^{\circ} n

Solution steps

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

Move

\frac{1}{2}

to the right side

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

Subtract

\frac{1}{2}

from both sides

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

Simplify

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

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

Divide both sides by

- 1

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

Divide both sides by

- 1

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

Simplify

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

Simplify

\frac{- sin ( x )}{- 1} : sin (x)

\frac{- sin ( x )}{- 1}

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

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

Apply rule

\frac{a}{1} = a

= sin (x)

Simplify

\frac{- \frac{1}{2}}{- 1} : \frac{1}{2}

\frac{- \frac{1}{2}}{- 1}

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

= \frac{\frac{1}{2}}{1}

Apply the fraction rule:

\frac{a}{1} = a

= \frac{1}{2}

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

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

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

General solutions for

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

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

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

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

2 sin^{2} (x) = 3 cos^{2} (x)

sin (2 x) - cos (2 x) = 1 + sin (x) - cos (x)

4 cos (2 θ) = 2 sin (θ) + 3

tan^{2} (x) - \frac{1}{3} = 0

sin (x) + cos^{2} (x) = 1

What is the general solution for 1/2-sin(x)=0 ?
The general solution for 1/2-sin(x)=0 is x= pi/6+2pin,x=(5pi)/6+2pin