What is the general solution for sin(pi/(11))=sin((xpi)/(11)) ?

The general solution for sin(pi/(11))=sin((xpi)/(11)) is x=1+22n,x=10+22n

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Popular Trigonometry >

sin(pi/(11))=sin((xpi)/(11))

Solution

sin (\frac{π}{11}) = sin (\frac{x π}{11})

Solution

x = 1 + 22 n, x = 10 + 22 n

Degrees

x = 57.29577 \dots^{\circ} + 1260.50714 \dots^{\circ} n, x = 572.95779 \dots^{\circ} + 1260.50714 \dots^{\circ} n

Solution steps

sin (\frac{π}{11}) = sin (\frac{x π}{11})

Switch sides

sin (\frac{x π}{11}) = sin (\frac{π}{11})

Apply trig inverse properties

sin (\frac{x π}{11}) = sin (\frac{π}{11})

General solutions for

sin (\frac{x π}{11}) = sin (\frac{π}{11})

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

\frac{x π}{11} = arcsin (sin (\frac{π}{11})) + 2 πn, \frac{x π}{11} = π - arcsin (sin (\frac{π}{11})) + 2 πn

\frac{x π}{11} = arcsin (sin (\frac{π}{11})) + 2 πn, \frac{x π}{11} = π - arcsin (sin (\frac{π}{11})) + 2 πn

Solve

\frac{x π}{11} = arcsin (sin (\frac{π}{11})) + 2 πn : x = 1 + 22 n

\frac{x π}{11} = arcsin (sin (\frac{π}{11})) + 2 πn

arcsin (sin (\frac{π}{11})) = \frac{π}{11}

arcsin (sin (\frac{π}{11}))

For

- \frac{π}{2} \leq x \leq \frac{π}{2}, a rcs in (s in (x)) = x

- \frac{π}{2} \leq \frac{π}{11} \leq \frac{π}{2}

= \frac{π}{11}

\frac{x π}{11} = \frac{π}{11} + 2 πn

Multiply both sides by

11

\frac{x π}{11} = \frac{π}{11} + 2 πn

Multiply both sides by

11

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

Simplify

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

Simplify

\frac{11 x π}{11} : π x

\frac{11 x π}{11}

Divide the numbers:

\frac{11}{11} = 1

= π x

Simplify

11 \cdot \frac{π}{11} + 11 \cdot 2 πn : π + 22 πn

11 \cdot \frac{π}{11} + 11 \cdot 2 πn

11 \cdot \frac{π}{11} = π

11 \cdot \frac{π}{11}

Multiply fractions:

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

= \frac{π 11}{11}

Cancel the common factor:

11

= π

11 \cdot 2 πn = 22 πn

11 \cdot 2 πn

Multiply the numbers:

11 \cdot 2 = 22

= 22 πn

= π + 22 πn

π x = π + 22 πn

π x = π + 22 πn

π x = π + 22 πn

Divide both sides by

π

π x = π + 22 πn

Divide both sides by

π

\frac{π x}{π} = \frac{π}{π} + \frac{22 πn}{π}

Simplify

\frac{π x}{π} = \frac{π}{π} + \frac{22 πn}{π}

Simplify

\frac{π x}{π} : x

\frac{π x}{π}

Cancel the common factor:

π

= x

Simplify

\frac{π}{π} + \frac{22 πn}{π} : 1 + 22 n

\frac{π}{π} + \frac{22 πn}{π}

Apply rule

\frac{a}{a} = 1

\frac{π}{π} = 1

= 1 + \frac{22 πn}{π}

Cancel

\frac{22 πn}{π} : 22 n

\frac{22 πn}{π}

Cancel the common factor:

π

= 22 n

= 1 + 22 n

x = 1 + 22 n

x = 1 + 22 n

x = 1 + 22 n

Solve

\frac{x π}{11} = π - arcsin (sin (\frac{π}{11})) + 2 πn : x = 10 + 22 n

\frac{x π}{11} = π - arcsin (sin (\frac{π}{11})) + 2 πn

arcsin (sin (\frac{π}{11})) = \frac{π}{11}

arcsin (sin (\frac{π}{11}))

For

- \frac{π}{2} \leq x \leq \frac{π}{2}, a rcs in (s in (x)) = x

- \frac{π}{2} \leq \frac{π}{11} \leq \frac{π}{2}

= \frac{π}{11}

\frac{x π}{11} = π - \frac{π}{11} + 2 πn

Multiply both sides by

11

\frac{x π}{11} = π - \frac{π}{11} + 2 πn

Multiply both sides by

11

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

Simplify

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

Simplify

\frac{11 x π}{11} : π x

\frac{11 x π}{11}

Divide the numbers:

\frac{11}{11} = 1

= π x

Simplify

11 π - 11 \cdot \frac{π}{11} + 11 \cdot 2 πn : 10 π + 22 πn

11 π - 11 \cdot \frac{π}{11} + 11 \cdot 2 πn

11 \cdot \frac{π}{11} = π

11 \cdot \frac{π}{11}

Multiply fractions:

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

= \frac{π 11}{11}

Cancel the common factor:

11

= π

11 \cdot 2 πn = 22 πn

11 \cdot 2 πn

Multiply the numbers:

11 \cdot 2 = 22

= 22 πn

= 11 π - π + 22 πn

Add similar elements:

11 π - π = 10 π

= 10 π + 22 πn

π x = 10 π + 22 πn

π x = 10 π + 22 πn

π x = 10 π + 22 πn

Divide both sides by

π

π x = 10 π + 22 πn

Divide both sides by

π

\frac{π x}{π} = \frac{10 π}{π} + \frac{22 πn}{π}

Simplify

\frac{π x}{π} = \frac{10 π}{π} + \frac{22 πn}{π}

Simplify

\frac{π x}{π} : x

\frac{π x}{π}

Cancel the common factor:

π

= x

Simplify

\frac{10 π}{π} + \frac{22 πn}{π} : 10 + 22 n

\frac{10 π}{π} + \frac{22 πn}{π}

Cancel

\frac{10 π}{π} : 10

\frac{10 π}{π}

Cancel the common factor:

π

= 10

= 10 + \frac{22 πn}{π}

Cancel

\frac{22 πn}{π} : 22 n

\frac{22 πn}{π}

Cancel the common factor:

π

= 22 n

= 10 + 22 n

x = 10 + 22 n

x = 10 + 22 n

x = 10 + 22 n

x = 1 + 22 n, x = 10 + 22 n

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for sin(pi/(11))=sin((xpi)/(11)) ?
The general solution for sin(pi/(11))=sin((xpi)/(11)) is x=1+22n,x=10+22n