What is the general solution for 561024=300*(1-cos(x/2)) ?

The general solution for 561024=300*(1-cos(x/2)) is No Solution for x\in\mathbb{R}

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Popular >

561024=300*(1-cos(x/2))

Solution

561024 = 300 \cdot (1 - cos (\frac{x}{2}))

Solution

No Solution for x \in R

Solution steps

561024 = 300 (1 - cos (\frac{x}{2}))

Switch sides

300 (1 - cos (\frac{x}{2})) = 561024

Divide both sides by

300

300 (1 - cos (\frac{x}{2})) = 561024

Divide both sides by

300

\frac{300 ( 1 - cos ( \frac{x}{2} ) )}{300} = \frac{561024}{300}

Simplify

1 - cos (\frac{x}{2}) = \frac{46752}{25}

1 - cos (\frac{x}{2}) = \frac{46752}{25}

Move

1

to the right side

1 - cos (\frac{x}{2}) = \frac{46752}{25}

Subtract

1

from both sides

1 - cos (\frac{x}{2}) - 1 = \frac{46752}{25} - 1

Simplify

1 - cos (\frac{x}{2}) - 1 = \frac{46752}{25} - 1

Simplify

1 - cos (\frac{x}{2}) - 1 : - cos (\frac{x}{2})

1 - cos (\frac{x}{2}) - 1

Add similar elements:

1 - 1 = 0

= - cos (\frac{x}{2})

Simplify

\frac{46752}{25} - 1 : \frac{46727}{25}

\frac{46752}{25} - 1

Convert element to fraction:

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

= - \frac{1 \cdot 25}{25} + \frac{46752}{25}

Since the denominators are equal, combine the fractions:

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

= \frac{- 1 \cdot 25 + 46752}{25}

- 1 \cdot 25 + 46752 = 46727

- 1 \cdot 25 + 46752

Multiply the numbers:

1 \cdot 25 = 25

= - 25 + 46752

Add/Subtract the numbers:

- 25 + 46752 = 46727

= 46727

= \frac{46727}{25}

- cos (\frac{x}{2}) = \frac{46727}{25}

- cos (\frac{x}{2}) = \frac{46727}{25}

- cos (\frac{x}{2}) = \frac{46727}{25}

Divide both sides by

- 1

- cos (\frac{x}{2}) = \frac{46727}{25}

Divide both sides by

- 1

\frac{- cos ( \frac{x}{2} )}{- 1} = \frac{\frac{46727}{25}}{- 1}

Simplify

\frac{- cos ( \frac{x}{2} )}{- 1} = \frac{\frac{46727}{25}}{- 1}

Simplify

\frac{- cos ( \frac{x}{2} )}{- 1} : cos (\frac{x}{2})

\frac{- cos ( \frac{x}{2} )}{- 1}

Apply the fraction rule:

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

= \frac{cos ( \frac{x}{2} )}{1}

Apply rule

\frac{a}{1} = a

= cos (\frac{x}{2})

Simplify

\frac{\frac{46727}{25}}{- 1} : - \frac{46727}{25}

\frac{\frac{46727}{25}}{- 1}

Apply the fraction rule:

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

= - \frac{\frac{46727}{25}}{1}

Apply the fraction rule:

\frac{a}{1} = a

\frac{\frac{46727}{25}}{1} = \frac{46727}{25}

= - \frac{46727}{25}

cos (\frac{x}{2}) = - \frac{46727}{25}

cos (\frac{x}{2}) = - \frac{46727}{25}

cos (\frac{x}{2}) = - \frac{46727}{25}

- 1 \leq cos (x) \leq 1

No Solution for x \in R

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for 561024=300*(1-cos(x/2)) ?
The general solution for 561024=300*(1-cos(x/2)) is No Solution for x\in\mathbb{R}