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Popular >

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

Solution

solve for

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

Solution

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

Solution steps

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

Switch sides

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

Remove parentheses:

(a) = a

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

Apply trig inverse properties

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

General solutions for

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

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

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

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

Solve

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

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

Multiply both sides by

x^{2}

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

Multiply both sides by

x^{2}

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

Simplify

1 = arccos (f g) x^{2} + 2 πn x^{2}

1 = arccos (f g) x^{2} + 2 πn x^{2}

Solve

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

1 = arccos (f g) x^{2} + 2 πn x^{2}

Switch sides

arccos (f g) x^{2} + 2 πn x^{2} = 1

Factor

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

arccos (f g) x^{2} + 2 πn x^{2}

Factor out common term

x^{2}

= x^{2} (arccos (f g) + 2 πn)

x^{2} (arccos (f g) + 2 πn) = 1

Divide both sides by

arccos (f g) + 2 πn; f \neq = \frac{cos ( - 2 πn )}{g}

x^{2} (arccos (f g) + 2 πn) = 1

Divide both sides by

arccos (f g) + 2 πn; f \neq = \frac{cos ( - 2 πn )}{g}

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

Simplify

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

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

For

x^{2} = f (a)

the solutions are

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

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

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

Solve

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

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

Multiply both sides by

x^{2}

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

Multiply both sides by

x^{2}

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

Simplify

1 = - arccos (f g) x^{2} + 2 πn x^{2}

1 = - arccos (f g) x^{2} + 2 πn x^{2}

Solve

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

1 = - arccos (f g) x^{2} + 2 πn x^{2}

Switch sides

- arccos (f g) x^{2} + 2 πn x^{2} = 1

Factor

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

- arccos (f g) x^{2} + 2 πn x^{2}

Factor out common term

x^{2}

= x^{2} (- arccos (f g) + 2 πn)

x^{2} (- arccos (f g) + 2 πn) = 1

Divide both sides by

- arccos (f g) + 2 πn; f \neq = \frac{cos ( 2 πn )}{g}

x^{2} (- arccos (f g) + 2 πn) = 1

Divide both sides by

- arccos (f g) + 2 πn; f \neq = \frac{cos ( 2 πn )}{g}

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

Simplify

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

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

For

x^{2} = f (a)

the solutions are

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

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

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

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

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