What is the general solution for 18617=(50)/(2pi)*(1+1-1-cos(x)) ?

The general solution for 18617=(50)/(2pi)*(1+1-1-cos(x)) is No Solution for x\in\mathbb{R}

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18617=(50)/(2pi)*(1+1-1-cos(x))

Solution

18617 = \frac{50}{2 π} \cdot (1 + 1 - 1 - cos (x))

Solution

No Solution for x \in R

Solution steps

18617 = \frac{50}{2 π} (1 + 1 - 1 - cos (x))

Switch sides

\frac{50}{2 π} (1 + 1 - 1 - cos (x)) = 18617

Multiply both sides by

π

\frac{50}{2 π} (1 + 1 - 1 - cos (x)) = 18617

Multiply both sides by

π

\frac{50}{2 π} (1 + 1 - 1 - cos (x)) π = 18617 π

Simplify

25 (- cos (x) + 1) = 18617 π

25 (- cos (x) + 1) = 18617 π

Divide both sides by

25

25 (- cos (x) + 1) = 18617 π

Divide both sides by

25

\frac{25 ( - cos ( x ) + 1 )}{25} = \frac{18617 π}{25}

Simplify

- cos (x) + 1 = \frac{18617 π}{25}

- cos (x) + 1 = \frac{18617 π}{25}

Move

1

to the right side

- cos (x) + 1 = \frac{18617 π}{25}

Subtract

1

from both sides

- cos (x) + 1 - 1 = \frac{18617 π}{25} - 1

Simplify

- cos (x) = \frac{18617 π}{25} - 1

- cos (x) = \frac{18617 π}{25} - 1

Divide both sides by

- 1

- cos (x) = \frac{18617 π}{25} - 1

Divide both sides by

- 1

\frac{- cos ( x )}{- 1} = \frac{\frac{18617 π}{25}}{- 1} - \frac{1}{- 1}

Simplify

\frac{- cos ( x )}{- 1} = \frac{\frac{18617 π}{25}}{- 1} - \frac{1}{- 1}

Simplify

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

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

Apply the fraction rule:

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

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

Apply rule

\frac{a}{1} = a

= cos (x)

Simplify

\frac{\frac{18617 π}{25}}{- 1} - \frac{1}{- 1} : - \frac{18617 π - 25}{25}

\frac{\frac{18617 π}{25}}{- 1} - \frac{1}{- 1}

Apply rule

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

= \frac{\frac{18617 π}{25} - 1}{- 1}

Apply the fraction rule:

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

= - \frac{\frac{18617 π}{25} - 1}{1}

Join

\frac{18617 π}{25} - 1 : \frac{18617 π - 25}{25}

\frac{18617 π}{25} - 1

Convert element to fraction:

1 = \frac{1 \cdot 25}{25}

= \frac{18617 π}{25} - \frac{1 \cdot 25}{25}

Since the denominators are equal, combine the fractions:

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

= \frac{18617 π - 1 \cdot 25}{25}

Multiply the numbers:

1 \cdot 25 = 25

= \frac{18617 π - 25}{25}

= - \frac{\frac{18617 π - 25}{25}}{1}

Apply the fraction rule:

\frac{a}{1} = a

= - \frac{18617 π - 25}{25}

cos (x) = - \frac{18617 π - 25}{25}

cos (x) = - \frac{18617 π - 25}{25}

cos (x) = - \frac{18617 π - 25}{25}

- 1 \leq cos (x) \leq 1

No Solution for x \in R

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Frequently Asked Questions (FAQ)

What is the general solution for 18617=(50)/(2pi)*(1+1-1-cos(x)) ?
The general solution for 18617=(50)/(2pi)*(1+1-1-cos(x)) is No Solution for x\in\mathbb{R}