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Popular >

solvefor x,f=cos(1/(x^2))

Solution

solve for

x, f = cos (\frac{1}{x ^{2}})

Solution

x = \frac{1}{arccos ( f ) + 2 πn}, x = - \frac{1}{arccos ( f ) + 2 πn}, x = \frac{1}{- arccos ( f ) + 2 πn}, x = - \frac{1}{- arccos ( f ) + 2 πn}

Solution steps

f = cos (\frac{1}{x ^{2}})

Switch sides

cos (\frac{1}{x ^{2}}) = f

Apply trig inverse properties

cos (\frac{1}{x ^{2}}) = f

General solutions for

cos (\frac{1}{x ^{2}}) = f

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = - arccos (a) + 2 πn

\frac{1}{x ^{2}} = arccos (f) + 2 πn, \frac{1}{x ^{2}} = - arccos (f) + 2 πn

\frac{1}{x ^{2}} = arccos (f) + 2 πn, \frac{1}{x ^{2}} = - arccos (f) + 2 πn

Solve

\frac{1}{x ^{2}} = arccos (f) + 2 πn : x = \frac{1}{arccos ( f ) + 2 πn}, x = - \frac{1}{arccos ( f ) + 2 πn}

\frac{1}{x ^{2}} = arccos (f) + 2 πn

Multiply both sides by

x^{2}

\frac{1}{x ^{2}} = arccos (f) + 2 πn

Multiply both sides by

x^{2}

\frac{1}{x ^{2}} x^{2} = arccos (f) x^{2} + 2 πn x^{2}

Simplify

1 = arccos (f) x^{2} + 2 πn x^{2}

1 = arccos (f) x^{2} + 2 πn x^{2}

Solve

1 = arccos (f) x^{2} + 2 πn x^{2} : x = \frac{1}{arccos ( f ) + 2 πn}, x = - \frac{1}{arccos ( f ) + 2 πn}

1 = arccos (f) x^{2} + 2 πn x^{2}

Switch sides

arccos (f) x^{2} + 2 πn x^{2} = 1

Factor

arccos (f) x^{2} + 2 πn x^{2} : x^{2} (arccos (f) + 2 πn)

arccos (f) x^{2} + 2 πn x^{2}

Factor out common term

x^{2}

= x^{2} (arccos (f) + 2 πn)

x^{2} (arccos (f) + 2 πn) = 1

Divide both sides by

arccos (f) + 2 πn

x^{2} (arccos (f) + 2 πn) = 1

Divide both sides by

arccos (f) + 2 πn

\frac{x ^{2} ( arccos ( f ) + 2 πn )}{arccos ( f ) + 2 πn} = \frac{1}{arccos ( f ) + 2 πn}

Simplify

x^{2} = \frac{1}{arccos ( f ) + 2 πn}

x^{2} = \frac{1}{arccos ( f ) + 2 πn}

For

x^{2} = f (a)

the solutions are

x = f (a), - f (a)

x = \frac{1}{arccos ( f ) + 2 πn}, x = - \frac{1}{arccos ( f ) + 2 πn}

x = \frac{1}{arccos ( f ) + 2 πn}, x = - \frac{1}{arccos ( f ) + 2 πn}

Solve

\frac{1}{x ^{2}} = - arccos (f) + 2 πn : x = \frac{1}{- arccos ( f ) + 2 πn}, x = - \frac{1}{- arccos ( f ) + 2 πn}

\frac{1}{x ^{2}} = - arccos (f) + 2 πn

Multiply both sides by

x^{2}

\frac{1}{x ^{2}} = - arccos (f) + 2 πn

Multiply both sides by

x^{2}

\frac{1}{x ^{2}} x^{2} = - arccos (f) x^{2} + 2 πn x^{2}

Simplify

1 = - arccos (f) x^{2} + 2 πn x^{2}

1 = - arccos (f) x^{2} + 2 πn x^{2}

Solve

1 = - arccos (f) x^{2} + 2 πn x^{2} : x = \frac{1}{- arccos ( f ) + 2 πn}, x = - \frac{1}{- arccos ( f ) + 2 πn}

1 = - arccos (f) x^{2} + 2 πn x^{2}

Switch sides

- arccos (f) x^{2} + 2 πn x^{2} = 1

Factor

- arccos (f) x^{2} + 2 πn x^{2} : x^{2} (- arccos (f) + 2 πn)

- arccos (f) x^{2} + 2 πn x^{2}

Factor out common term

x^{2}

= x^{2} (- arccos (f) + 2 πn)

x^{2} (- arccos (f) + 2 πn) = 1

Divide both sides by

- arccos (f) + 2 πn

x^{2} (- arccos (f) + 2 πn) = 1

Divide both sides by

- arccos (f) + 2 πn

\frac{x ^{2} ( - arccos ( f ) + 2 πn )}{- arccos ( f ) + 2 πn} = \frac{1}{- arccos ( f ) + 2 πn}

Simplify

x^{2} = \frac{1}{- arccos ( f ) + 2 πn}

x^{2} = \frac{1}{- arccos ( f ) + 2 πn}

For

x^{2} = f (a)

the solutions are

x = f (a), - f (a)

x = \frac{1}{- arccos ( f ) + 2 πn}, x = - \frac{1}{- arccos ( f ) + 2 πn}

x = \frac{1}{- arccos ( f ) + 2 πn}, x = - \frac{1}{- arccos ( f ) + 2 πn}

x = \frac{1}{arccos ( f ) + 2 πn}, x = - \frac{1}{arccos ( f ) + 2 πn}, x = \frac{1}{- arccos ( f ) + 2 πn}, x = - \frac{1}{- arccos ( f ) + 2 πn}

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