What is the general solution for solvefor x,2sin((pi(x-2))/6)=1 ?

The general solution for solvefor x,2sin((pi(x-2))/6)=1 is x=12n+3,x=12n+7

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Trigonometry >

solvefor x,2sin((pi(x-2))/6)=1

Solution

solvefor

Solution

x = 12 n + 3, x = 12 n + 7

Degrees

x = 171.88733 \dots^{\circ} + 687.54935 \dots^{\circ} n, x = 401.07045 \dots^{\circ} + 687.54935 \dots^{\circ} n

Solution steps

2 sin (\frac{π ( x - 2 )}{6}) = 1

Divide both sides by

2

2 sin (\frac{π ( x - 2 )}{6}) = 1

Divide both sides by

2

\frac{2 sin ( \frac{π ( x - 2 )}{6} )}{2} = \frac{1}{2}

Simplify

sin (\frac{π ( x - 2 )}{6}) = \frac{1}{2}

sin (\frac{π ( x - 2 )}{6}) = \frac{1}{2}

General solutions for

sin (\frac{π ( x - 2 )}{6}) = \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}

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

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

Solve

\frac{π ( x - 2 )}{6} = \frac{π}{6} + 2 πn : x = 12 n + 3

\frac{π ( x - 2 )}{6} = \frac{π}{6} + 2 πn

Multiply both sides by

6

\frac{π ( x - 2 )}{6} = \frac{π}{6} + 2 πn

Multiply both sides by

6

\frac{6 π ( x - 2 )}{6} = 6 \cdot \frac{π}{6} + 6 \cdot 2 πn

Simplify

\frac{6 π ( x - 2 )}{6} = 6 \cdot \frac{π}{6} + 6 \cdot 2 πn

Simplify

\frac{6 π ( x - 2 )}{6} : π (x - 2)

\frac{6 π ( x - 2 )}{6}

Divide the numbers:

\frac{6}{6} = 1

= π (x - 2)

Simplify

6 \cdot \frac{π}{6} + 6 \cdot 2 πn : π + 12 πn

6 \cdot \frac{π}{6} + 6 \cdot 2 πn

6 \cdot \frac{π}{6} = π

6 \cdot \frac{π}{6}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{π 6}{6}

Cancel the common factor:

6

= π

6 \cdot 2 πn = 12 πn

6 \cdot 2 πn

Multiply the numbers:

6 \cdot 2 = 12

= 12 πn

= π + 12 πn

π (x - 2) = π + 12 πn

π (x - 2) = π + 12 πn

π (x - 2) = π + 12 πn

Divide both sides by

π

π (x - 2) = π + 12 πn

Divide both sides by

π

\frac{π ( x - 2 )}{π} = \frac{π}{π} + \frac{12 πn}{π}

Simplify

\frac{π ( x - 2 )}{π} = \frac{π}{π} + \frac{12 πn}{π}

Simplify

\frac{π ( x - 2 )}{π} : x - 2

\frac{π ( x - 2 )}{π}

Cancel the common factor:

π

= x - 2

Simplify

\frac{π}{π} + \frac{12 πn}{π} : 1 + 12 n

\frac{π}{π} + \frac{12 πn}{π}

Apply rule

\frac{a}{a} = 1

\frac{π}{π} = 1

= 1 + \frac{12 πn}{π}

Cancel

\frac{12 πn}{π} : 12 n

\frac{12 πn}{π}

Cancel the common factor:

π

= 12 n

= 1 + 12 n

x - 2 = 1 + 12 n

x - 2 = 1 + 12 n

x - 2 = 1 + 12 n

Move

2

to the right side

x - 2 = 1 + 12 n

Add

2

to both sides

x - 2 + 2 = 1 + 12 n + 2

Simplify

x = 12 n + 3

x = 12 n + 3

Solve

\frac{π ( x - 2 )}{6} = \frac{5 π}{6} + 2 πn : x = 12 n + 7

\frac{π ( x - 2 )}{6} = \frac{5 π}{6} + 2 πn

Multiply both sides by

6

\frac{π ( x - 2 )}{6} = \frac{5 π}{6} + 2 πn

Multiply both sides by

6

\frac{6 π ( x - 2 )}{6} = 6 \cdot \frac{5 π}{6} + 6 \cdot 2 πn

Simplify

\frac{6 π ( x - 2 )}{6} = 6 \cdot \frac{5 π}{6} + 6 \cdot 2 πn

Simplify

\frac{6 π ( x - 2 )}{6} : π (x - 2)

\frac{6 π ( x - 2 )}{6}

Divide the numbers:

\frac{6}{6} = 1

= π (x - 2)

Simplify

6 \cdot \frac{5 π}{6} + 6 \cdot 2 πn : 5 π + 12 πn

6 \cdot \frac{5 π}{6} + 6 \cdot 2 πn

6 \cdot \frac{5 π}{6} = 5 π

6 \cdot \frac{5 π}{6}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{5 π 6}{6}

Cancel the common factor:

6

= 5 π

6 \cdot 2 πn = 12 πn

6 \cdot 2 πn

Multiply the numbers:

6 \cdot 2 = 12

= 12 πn

= 5 π + 12 πn

π (x - 2) = 5 π + 12 πn

π (x - 2) = 5 π + 12 πn

π (x - 2) = 5 π + 12 πn

Divide both sides by

π

π (x - 2) = 5 π + 12 πn

Divide both sides by

π

\frac{π ( x - 2 )}{π} = \frac{5 π}{π} + \frac{12 πn}{π}

Simplify

\frac{π ( x - 2 )}{π} = \frac{5 π}{π} + \frac{12 πn}{π}

Simplify

\frac{π ( x - 2 )}{π} : x - 2

\frac{π ( x - 2 )}{π}

Cancel the common factor:

π

= x - 2

Simplify

\frac{5 π}{π} + \frac{12 πn}{π} : 5 + 12 n

\frac{5 π}{π} + \frac{12 πn}{π}

Cancel

\frac{5 π}{π} : 5

\frac{5 π}{π}

Cancel the common factor:

π

= 5

= 5 + \frac{12 πn}{π}

Cancel

\frac{12 πn}{π} : 12 n

\frac{12 πn}{π}

Cancel the common factor:

π

= 12 n

= 5 + 12 n

x - 2 = 5 + 12 n

x - 2 = 5 + 12 n

x - 2 = 5 + 12 n

Move

2

to the right side

x - 2 = 5 + 12 n

Add

2

to both sides

x - 2 + 2 = 5 + 12 n + 2

Simplify

x = 12 n + 7

x = 12 n + 7

x = 12 n + 3, x = 12 n + 7

Graph

Popular Examples

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

2cos(x)=cos^2(x)-1

2sin(v)csc(v)-csc(v)=4sin(v)-2

2cos(2x)=4cos(x)

(sin(42))/(22)=(sin(B))/(12)

Frequently Asked Questions (FAQ)

What is the general solution for solvefor x,2sin((pi(x-2))/6)=1 ?
The general solution for solvefor x,2sin((pi(x-2))/6)=1 is x=12n+3,x=12n+7