What is the general solution for 3.1=48.1(1-cos((28.66x)/(48.1))) ?

The general solution for 3.1=48.1(1-cos((28.66x)/(48.1))) is No Solution for x\in\mathbb{R}

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3.1=48.1(1-cos((28.66x)/(48.1)))

Solution

3.1 = 48.1 (1 - cos (\frac{28.66 x}{48.1}))

Solution

No Solution for x \in R

Solution steps

3.1 = 48.1 (1 - cos (\frac{28.66 x}{48.1}))

Switch sides

48.1 (1 - cos (\frac{28.66 x}{48.1})) = 3.1

Multiply both sides by

10

48.1 (1 - cos (\frac{28.66 x}{48.1})) = 3.1

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere is one digit to the right of the decimal point, therefore multiply by

10

48.1 (1 - cos (\frac{28.66 x}{48.1})) \cdot 10 = 3.1 \cdot 10

Refine

481 (1 - cos (\frac{28.66 x}{48.1})) = 31

481 (1 - cos (\frac{28.66 x}{48.1})) = 31

Divide both sides by

481

481 (1 - cos (\frac{28.66 x}{48.1})) = 31

Divide both sides by

481

\frac{481 ( 1 - cos ( \frac{28.66 x}{48.1} ) )}{481} = \frac{31}{481}

Simplify

1 - cos (\frac{28.66 x}{48.1}) = \frac{31}{481}

1 - cos (\frac{28.66 x}{48.1}) = \frac{31}{481}

Move

1

to the right side

1 - cos (\frac{28.66 x}{48.1}) = \frac{31}{481}

Subtract

1

from both sides

1 - cos (\frac{28.66 x}{48.1}) - 1 = \frac{31}{481} - 1

Simplify

1 - cos (\frac{28.66 x}{48.1}) - 1 = \frac{31}{481} - 1

Simplify

1 - cos (\frac{28.66 x}{48.1}) - 1 : - cos (\frac{28.66 x}{48.1})

1 - cos (\frac{28.66 x}{48.1}) - 1

Add similar elements:

1 - 1 = 0

= - cos (\frac{28.66 x}{48.1})

Simplify

\frac{31}{481} - 1 : - \frac{450}{481}

\frac{31}{481} - 1

Convert element to fraction:

1 = \frac{1 \cdot 481}{481}

= - \frac{1 \cdot 481}{481} + \frac{31}{481}

Since the denominators are equal, combine the fractions:

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

= \frac{- 1 \cdot 481 + 31}{481}

- 1 \cdot 481 + 31 = - 450

- 1 \cdot 481 + 31

Multiply the numbers:

1 \cdot 481 = 481

= - 481 + 31

Add/Subtract the numbers:

- 481 + 31 = - 450

= - 450

= \frac{- 450}{481}

Apply the fraction rule:

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

= - \frac{450}{481}

- cos (\frac{28.66 x}{48.1}) = - \frac{450}{481}

- cos (\frac{28.66 x}{48.1}) = - \frac{450}{481}

- cos (\frac{28.66 x}{48.1}) = - \frac{450}{481}

Divide both sides by

- 1

- cos (\frac{28.66 x}{48.1}) = - \frac{450}{481}

Divide both sides by

- 1

\frac{- cos ( \frac{28.66 x}{48.1} )}{- 1} = \frac{- \frac{450}{481}}{- 1}

Simplify

\frac{- cos ( \frac{28.66 x}{48.1} )}{- 1} = \frac{- \frac{450}{481}}{- 1}

Simplify

\frac{- cos ( \frac{28.66 x}{48.1} )}{- 1} : cos (\frac{28.66 x}{48.1})

\frac{- cos ( \frac{28.66 x}{48.1} )}{- 1}

Apply the fraction rule:

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

= \frac{cos ( \frac{28.66 x}{48.1} )}{1}

Apply rule

\frac{a}{1} = a

= cos (\frac{28.66 x}{48.1})

Simplify

\frac{- \frac{450}{481}}{- 1} : \frac{450}{481}

\frac{- \frac{450}{481}}{- 1}

Apply the fraction rule:

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

= \frac{\frac{450}{481}}{1}

Apply the fraction rule:

\frac{a}{1} = a

= \frac{450}{481}

cos (\frac{28.66 x}{48.1}) = \frac{450}{481}

cos (\frac{28.66 x}{48.1}) = \frac{450}{481}

cos (\frac{28.66 x}{48.1}) = \frac{450}{481}

Apply trig inverse properties

cos (\frac{28.66 x}{48.1}) = \frac{450}{481}

General solutions for

cos (\frac{28.66 x}{48.1}) = \frac{450}{481}

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

\frac{28.66 x}{48.1} = arccos (\frac{450}{481}) + 2 πn, \frac{28.66 x}{48.1} = 2 π - arccos (\frac{450}{481}) + 2 πn

\frac{28.66 x}{48.1} = arccos (\frac{450}{481}) + 2 πn, \frac{28.66 x}{48.1} = 2 π - arccos (\frac{450}{481}) + 2 πn

No Solution for x \in R

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Frequently Asked Questions (FAQ)

What is the general solution for 3.1=48.1(1-cos((28.66x)/(48.1))) ?
The general solution for 3.1=48.1(1-cos((28.66x)/(48.1))) is No Solution for x\in\mathbb{R}