What is the general solution for 185=(220sqrt(2))/pi-cos(pi)+cos(x) ?

The general solution for 185=(220sqrt(2))/pi-cos(pi)+cos(x) is No Solution for x\in\mathbb{R}

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185=(220sqrt(2))/pi-cos(pi)+cos(x)

Solution

185 = \frac{220 2}{π} - cos (π) + cos (x)

Solution

No Solution for x \in R

Solution steps

185 = \frac{220 2}{π} - cos (π) + cos (x)

Switch sides

\frac{220 2}{π} - cos (π) + cos (x) = 185

cos (π) = - 1

cos (π)

Use the following trivial identity:

cos (π) = (- 1)

cos (π)

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= (- 1)

= - 1

\frac{220 2}{π} - - 1 + cos (x) = 185

Move to the right side

\frac{220 2}{π} - - 1 + cos (x) = 185

Subtract

-

from both sides

\frac{220 2}{π} - - 1 + cos (x) = 185

Simplify

\frac{220 2}{π} - 1 + cos (x) = 185

\frac{220 2}{π} - 1 + cos (x) = 185

Move

\frac{220 2}{π}

to the right side

\frac{220 2}{π} - 1 + cos (x) = 185

Subtract

\frac{220 2}{π}

from both sides

\frac{220 2}{π} - 1 + cos (x) - \frac{220 2}{π} = 185 - \frac{220 2}{π}

Simplify

- 1 + cos (x) = 185 - \frac{220 2}{π}

- 1 + cos (x) = 185 - \frac{220 2}{π}

Move

1

to the right side

- 1 + cos (x) = 185 - \frac{220 2}{π}

Add

1

to both sides

- 1 + cos (x) + 1 = 185 - \frac{220 2}{π} + 1

Simplify

- 1 + cos (x) + 1 = 185 - \frac{220 2}{π} + 1

Simplify

- 1 + cos (x) + 1 : cos (x)

- 1 + cos (x) + 1

Add similar elements:

- 1 + 1 = 0

= cos (x)

Simplify

185 - \frac{220 2}{π} + 1 : - \frac{220 2}{π} + 186

185 - \frac{220 2}{π} + 1

Add the numbers:

185 + 1 = 186

= - \frac{220 2}{π} + 186

cos (x) = - \frac{220 2}{π} + 186

cos (x) = - \frac{220 2}{π} + 186

cos (x) = - \frac{220 2}{π} + 186

- 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 185=(220sqrt(2))/pi-cos(pi)+cos(x) ?
The general solution for 185=(220sqrt(2))/pi-cos(pi)+cos(x) is No Solution for x\in\mathbb{R}