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Popular >

sin(1/x)=-1/2

Solution

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

Solution

x = \frac{6}{π ( 7 + 12 n )}, x = \frac{6}{π ( 11 + 12 n )}; n \neq = - \frac{7}{12}, n \neq = - \frac{11}{12}

Degrees

x = 0^{\circ} + 5.75930 \dots^{\circ} n, x = 0^{\circ} + 4.75769 \dots^{\circ} n

Solution steps

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

General solutions for

sin (\frac{1}{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}

\frac{1}{x} = \frac{7 π}{6} + 2 πn, \frac{1}{x} = \frac{11 π}{6} + 2 πn

\frac{1}{x} = \frac{7 π}{6} + 2 πn, \frac{1}{x} = \frac{11 π}{6} + 2 πn

Solve

\frac{1}{x} = \frac{7 π}{6} + 2 πn : x = \frac{6}{π ( 7 + 12 n )}; n \neq = - \frac{7}{12}

\frac{1}{x} = \frac{7 π}{6} + 2 πn

Multiply both sides by

x

\frac{1}{x} = \frac{7 π}{6} + 2 πn

Multiply both sides by

x

\frac{1}{x} x = \frac{7 π}{6} x + 2 πn x

Simplify

1 = \frac{7 π}{6} x + 2 πn x

1 = \frac{7 π}{6} x + 2 πn x

Switch sides

\frac{7 π}{6} x + 2 πn x = 1

Multiply both sides by

6

\frac{7 π}{6} x + 2 πn x = 1

Multiply both sides by

6

\frac{7 π}{6} x \cdot 6 + 2 πn x \cdot 6 = 1 \cdot 6

Simplify

\frac{7 π}{6} x \cdot 6 + 2 πn x \cdot 6 = 1 \cdot 6

Simplify

\frac{7 π}{6} x \cdot 6 : 7 π x

\frac{7 π}{6} x \cdot 6

Multiply fractions:

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

= \frac{7 \cdot 6 π}{6} x

Cancel the common factor:

6

= x \cdot 7 π

Simplify

2 πn x \cdot 6 : 12 πn x

2 πn x \cdot 6

Multiply the numbers:

2 \cdot 6 = 12

= 12 πn x

Simplify

1 \cdot 6 : 6

1 \cdot 6

Multiply the numbers:

1 \cdot 6 = 6

= 6

7 π x + 12 πn x = 6

7 π x + 12 πn x = 6

7 π x + 12 πn x = 6

Factor

7 π x + 12 πn x : π x (7 + 12 n)

7 π x + 12 πn x

Factor out common term

x π

= x π (7 + 12 n)

π x (7 + 12 n) = 6

Divide both sides by

π (7 + 12 n); n \neq = - \frac{7}{12}

π x (7 + 12 n) = 6

Divide both sides by

π (7 + 12 n); n \neq = - \frac{7}{12}

\frac{π x ( 7 + 12 n )}{π ( 7 + 12 n )} = \frac{6}{π ( 7 + 12 n )}; n \neq = - \frac{7}{12}

Simplify

x = \frac{6}{π ( 7 + 12 n )}; n \neq = - \frac{7}{12}

x = \frac{6}{π ( 7 + 12 n )}; n \neq = - \frac{7}{12}

Solve

\frac{1}{x} = \frac{11 π}{6} + 2 πn : x = \frac{6}{π ( 11 + 12 n )}; n \neq = - \frac{11}{12}

\frac{1}{x} = \frac{11 π}{6} + 2 πn

Multiply both sides by

x

\frac{1}{x} = \frac{11 π}{6} + 2 πn

Multiply both sides by

x

\frac{1}{x} x = \frac{11 π}{6} x + 2 πn x

Simplify

1 = \frac{11 π}{6} x + 2 πn x

1 = \frac{11 π}{6} x + 2 πn x

Switch sides

\frac{11 π}{6} x + 2 πn x = 1

Multiply both sides by

6

\frac{11 π}{6} x + 2 πn x = 1

Multiply both sides by

6

\frac{11 π}{6} x \cdot 6 + 2 πn x \cdot 6 = 1 \cdot 6

Simplify

\frac{11 π}{6} x \cdot 6 + 2 πn x \cdot 6 = 1 \cdot 6

Simplify

\frac{11 π}{6} x \cdot 6 : 11 π x

\frac{11 π}{6} x \cdot 6

Multiply fractions:

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

= \frac{11 \cdot 6 π}{6} x

Cancel the common factor:

6

= x \cdot 11 π

Simplify

2 πn x \cdot 6 : 12 πn x

2 πn x \cdot 6

Multiply the numbers:

2 \cdot 6 = 12

= 12 πn x

Simplify

1 \cdot 6 : 6

1 \cdot 6

Multiply the numbers:

1 \cdot 6 = 6

= 6

11 π x + 12 πn x = 6

11 π x + 12 πn x = 6

11 π x + 12 πn x = 6

Factor

11 π x + 12 πn x : π x (11 + 12 n)

11 π x + 12 πn x

Factor out common term

x π

= x π (11 + 12 n)

π x (11 + 12 n) = 6

Divide both sides by

π (11 + 12 n); n \neq = - \frac{11}{12}

π x (11 + 12 n) = 6

Divide both sides by

π (11 + 12 n); n \neq = - \frac{11}{12}

\frac{π x ( 11 + 12 n )}{π ( 11 + 12 n )} = \frac{6}{π ( 11 + 12 n )}; n \neq = - \frac{11}{12}

Simplify

x = \frac{6}{π ( 11 + 12 n )}; n \neq = - \frac{11}{12}

x = \frac{6}{π ( 11 + 12 n )}; n \neq = - \frac{11}{12}

x = \frac{6}{π ( 7 + 12 n )}, x = \frac{6}{π ( 11 + 12 n )}; n \neq = - \frac{7}{12}, n \neq = - \frac{11}{12}

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