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Popular >

solvefor x,cos(2y-5x)=4y+5

Solution

solve for

x, cos (2 y - 5 x) = 4 y + 5

Solution

x = - \frac{arccos ( 4 y + 5 )}{5} - \frac{2 πn}{5} + \frac{2 y}{5}, x = \frac{arccos ( 4 y + 5 )}{5} - \frac{2 πn}{5} + \frac{2 y}{5}

Solution steps

cos (2 y - 5 x) = 4 y + 5

Apply trig inverse properties

cos (2 y - 5 x) = 4 y + 5

General solutions for

cos (2 y - 5 x) = 4 y + 5

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

2 y - 5 x = arccos (4 y + 5) + 2 πn, 2 y - 5 x = - arccos (4 y + 5) + 2 πn

2 y - 5 x = arccos (4 y + 5) + 2 πn, 2 y - 5 x = - arccos (4 y + 5) + 2 πn

Solve

2 y - 5 x = arccos (4 y + 5) + 2 πn : x = - \frac{arccos ( 4 y + 5 )}{5} - \frac{2 πn}{5} + \frac{2 y}{5}

2 y - 5 x = arccos (4 y + 5) + 2 πn

Move

2 y

to the right side

2 y - 5 x = arccos (4 y + 5) + 2 πn

Subtract

2 y

from both sides

2 y - 5 x - 2 y = arccos (4 y + 5) + 2 πn - 2 y

Simplify

- 5 x = arccos (4 y + 5) + 2 πn - 2 y

- 5 x = arccos (4 y + 5) + 2 πn - 2 y

Divide both sides by

- 5

- 5 x = arccos (4 y + 5) + 2 πn - 2 y

Divide both sides by

- 5

\frac{- 5 x}{- 5} = \frac{arccos ( 4 y + 5 )}{- 5} + \frac{2 πn}{- 5} - \frac{2 y}{- 5}

Simplify

\frac{- 5 x}{- 5} = \frac{arccos ( 4 y + 5 )}{- 5} + \frac{2 πn}{- 5} - \frac{2 y}{- 5}

Simplify

\frac{- 5 x}{- 5} : x

\frac{- 5 x}{- 5}

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

= \frac{5 x}{5}

Divide the numbers:

\frac{5}{5} = 1

= x

Simplify

\frac{arccos ( 4 y + 5 )}{- 5} + \frac{2 πn}{- 5} - \frac{2 y}{- 5} : - \frac{arccos ( 4 y + 5 )}{5} - \frac{2 πn}{5} + \frac{2 y}{5}

\frac{arccos ( 4 y + 5 )}{- 5} + \frac{2 πn}{- 5} - \frac{2 y}{- 5}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{arccos ( 4 y + 5 )}{5} + \frac{2 πn}{- 5} - \frac{2 y}{- 5}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{arccos ( 4 y + 5 )}{5} - \frac{2 πn}{5} - \frac{2 y}{- 5}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{arccos ( 4 y + 5 )}{5} - \frac{2 πn}{5} - (- \frac{2 y}{5})

Apply rule

- (- a) = a

= - \frac{arccos ( 4 y + 5 )}{5} - \frac{2 πn}{5} + \frac{2 y}{5}

x = - \frac{arccos ( 4 y + 5 )}{5} - \frac{2 πn}{5} + \frac{2 y}{5}

x = - \frac{arccos ( 4 y + 5 )}{5} - \frac{2 πn}{5} + \frac{2 y}{5}

x = - \frac{arccos ( 4 y + 5 )}{5} - \frac{2 πn}{5} + \frac{2 y}{5}

Solve

2 y - 5 x = - arccos (4 y + 5) + 2 πn : x = \frac{arccos ( 4 y + 5 )}{5} - \frac{2 πn}{5} + \frac{2 y}{5}

2 y - 5 x = - arccos (4 y + 5) + 2 πn

Move

2 y

to the right side

2 y - 5 x = - arccos (4 y + 5) + 2 πn

Subtract

2 y

from both sides

2 y - 5 x - 2 y = - arccos (4 y + 5) + 2 πn - 2 y

Simplify

- 5 x = - arccos (4 y + 5) + 2 πn - 2 y

- 5 x = - arccos (4 y + 5) + 2 πn - 2 y

Divide both sides by

- 5

- 5 x = - arccos (4 y + 5) + 2 πn - 2 y

Divide both sides by

- 5

\frac{- 5 x}{- 5} = - \frac{arccos ( 4 y + 5 )}{- 5} + \frac{2 πn}{- 5} - \frac{2 y}{- 5}

Simplify

\frac{- 5 x}{- 5} = - \frac{arccos ( 4 y + 5 )}{- 5} + \frac{2 πn}{- 5} - \frac{2 y}{- 5}

Simplify

\frac{- 5 x}{- 5} : x

\frac{- 5 x}{- 5}

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

= \frac{5 x}{5}

Divide the numbers:

\frac{5}{5} = 1

= x

Simplify

- \frac{arccos ( 4 y + 5 )}{- 5} + \frac{2 πn}{- 5} - \frac{2 y}{- 5} : \frac{arccos ( 4 y + 5 )}{5} - \frac{2 πn}{5} + \frac{2 y}{5}

- \frac{arccos ( 4 y + 5 )}{- 5} + \frac{2 πn}{- 5} - \frac{2 y}{- 5}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - (- \frac{arccos ( 4 y + 5 )}{5}) + \frac{2 πn}{- 5} - \frac{2 y}{- 5}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - (- \frac{arccos ( 4 y + 5 )}{5}) - \frac{2 πn}{5} - \frac{2 y}{- 5}

Apply rule

- (- a) = a

= \frac{arccos ( 4 y + 5 )}{5} - \frac{2 πn}{5} - \frac{2 y}{- 5}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= \frac{arccos ( 4 y + 5 )}{5} - \frac{2 πn}{5} - (- \frac{2 y}{5})

Apply rule

- (- a) = a

= \frac{arccos ( 4 y + 5 )}{5} - \frac{2 πn}{5} + \frac{2 y}{5}

x = \frac{arccos ( 4 y + 5 )}{5} - \frac{2 πn}{5} + \frac{2 y}{5}

x = \frac{arccos ( 4 y + 5 )}{5} - \frac{2 πn}{5} + \frac{2 y}{5}

x = \frac{arccos ( 4 y + 5 )}{5} - \frac{2 πn}{5} + \frac{2 y}{5}

x = - \frac{arccos ( 4 y + 5 )}{5} - \frac{2 πn}{5} + \frac{2 y}{5}, x = \frac{arccos ( 4 y + 5 )}{5} - \frac{2 πn}{5} + \frac{2 y}{5}

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