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Popular >

solvefor x,cos(x^3y^3)=5y^3

Solution

solve for

x, cos (x^{3} y^{3}) = 5 y^{3}

Solution

Solution steps

cos (x^{3} y^{3}) = 5 y^{3}

Apply trig inverse properties

cos (x^{3} y^{3}) = 5 y^{3}

General solutions for

cos (x^{3} y^{3}) = 5 y^{3}

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

x^{3} y^{3} = arccos (5 y^{3}) + 2 πn, x^{3} y^{3} = - arccos (5 y^{3}) + 2 πn

x^{3} y^{3} = arccos (5 y^{3}) + 2 πn, x^{3} y^{3} = - arccos (5 y^{3}) + 2 πn

Solve

x^{3} y^{3} = arccos (5 y^{3}) + 2 πn

Divide both sides by

y^{3}; y \neq = 0

x^{3} y^{3} = arccos (5 y^{3}) + 2 πn

Divide both sides by

y^{3}; y \neq = 0

\frac{x ^{3} y ^{3}}{y ^{3}} = \frac{arccos ( 5 y ^{3} )}{y ^{3}} + \frac{2 πn}{y ^{3}}; y \neq = 0

Simplify

x^{3} = \frac{arccos ( 5 y ^{3} )}{y ^{3}} + \frac{2 πn}{y ^{3}}; y \neq = 0

x^{3} = \frac{arccos ( 5 y ^{3} )}{y ^{3}} + \frac{2 πn}{y ^{3}}; y \neq = 0

For

x^{n} = f (a)

, n is odd, the solution is

Simplify

Combine the fractions

\frac{arccos ( 5 y ^{3} )}{y ^{3}} + \frac{2 πn}{y ^{3}} : \frac{arccos ( 5 y ^{3} ) + 2 πn}{y ^{3}}

Apply rule

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

= \frac{arccos ( 5 y ^{3} ) + 2 πn}{y ^{3}}

Apply radical rule:

assuming

a \geq 0, b \geq 0

Apply radical rule:

assuming

a \geq 0

Solve

x^{3} y^{3} = - arccos (5 y^{3}) + 2 πn

Divide both sides by

y^{3}; y \neq = 0

x^{3} y^{3} = - arccos (5 y^{3}) + 2 πn

Divide both sides by

y^{3}; y \neq = 0

\frac{x ^{3} y ^{3}}{y ^{3}} = - \frac{arccos ( 5 y ^{3} )}{y ^{3}} + \frac{2 πn}{y ^{3}}; y \neq = 0

Simplify

x^{3} = - \frac{arccos ( 5 y ^{3} )}{y ^{3}} + \frac{2 πn}{y ^{3}}; y \neq = 0

x^{3} = - \frac{arccos ( 5 y ^{3} )}{y ^{3}} + \frac{2 πn}{y ^{3}}; y \neq = 0

For

x^{n} = f (a)

, n is odd, the solution is

Simplify

Combine the fractions

- \frac{arccos ( 5 y ^{3} )}{y ^{3}} + \frac{2 πn}{y ^{3}} : \frac{- arccos ( 5 y ^{3} ) + 2 πn}{y ^{3}}

Apply rule

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

= \frac{- arccos ( 5 y ^{3} ) + 2 πn}{y ^{3}}

Apply radical rule:

assuming

a \geq 0, b \geq 0

Apply radical rule:

assuming

a \geq 0

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