What is the general solution for (12000}{2*6380}=tan(\frac{90-u)/2) ?

The general solution for (12000}{2*6380}=tan(\frac{90-u)/2) is u=-360n+90-2*0.75471…

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(12000}{2*6380}=tan(\frac{90-u)/2)

Solution

\frac{12000}{2 \cdot 6380} = tan (\frac{9 0 ^{\circ} - u}{2})

Solution

u = - 36 0^{\circ} n + 9 0^{\circ} - 2 \cdot 0.75471 \dots

Radians

u = \frac{π}{2} - 2 \cdot 0.75471 \dots - 2 πn

Solution steps

\frac{12000}{2 \cdot 6380} = tan (\frac{9 0 ^{\circ} - u}{2})

Switch sides

tan (\frac{9 0 ^{\circ} - u}{2}) = \frac{12000}{2 \cdot 6380}

Simplify

\frac{12000}{2 \cdot 6380} : \frac{300}{319}

\frac{12000}{2 \cdot 6380}

Multiply the numbers:

2 \cdot 6380 = 12760

= \frac{12000}{12760}

Cancel the common factor:

40

= \frac{300}{319}

Apply trig inverse properties

tan (\frac{9 0 ^{\circ} - u}{2}) = \frac{300}{319}

General solutions for

tan (\frac{9 0 ^{\circ} - u}{2}) = \frac{300}{319}

tan (x) = a \Rightarrow x = arctan (a) + 18 0^{\circ} n

\frac{9 0 ^{\circ} - u}{2} = arctan (\frac{300}{319}) + 18 0^{\circ} n

\frac{9 0 ^{\circ} - u}{2} = arctan (\frac{300}{319}) + 18 0^{\circ} n

Solve

\frac{9 0 ^{\circ} - u}{2} = arctan (\frac{300}{319}) + 18 0^{\circ} n : u = - 36 0^{\circ} n + 9 0^{\circ} - 2 arctan (\frac{300}{319})

\frac{9 0 ^{\circ} - u}{2} = arctan (\frac{300}{319}) + 18 0^{\circ} n

Multiply both sides by

2

\frac{9 0 ^{\circ} - u}{2} = arctan (\frac{300}{319}) + 18 0^{\circ} n

Multiply both sides by

2

\frac{2 ( 9 0 ^{\circ} - u )}{2} = 2 arctan (\frac{300}{319}) + 36 0^{\circ} n

Simplify

9 0^{\circ} - u = 2 arctan (\frac{300}{319}) + 36 0^{\circ} n

9 0^{\circ} - u = 2 arctan (\frac{300}{319}) + 36 0^{\circ} n

Move

9 0^{\circ}

to the right side

9 0^{\circ} - u = 2 arctan (\frac{300}{319}) + 36 0^{\circ} n

Subtract

9 0^{\circ}

from both sides

9 0^{\circ} - u - 9 0^{\circ} = 2 arctan (\frac{300}{319}) + 36 0^{\circ} n - 9 0^{\circ}

Simplify

- u = 2 arctan (\frac{300}{319}) + 36 0^{\circ} n - 9 0^{\circ}

- u = 2 arctan (\frac{300}{319}) + 36 0^{\circ} n - 9 0^{\circ}

Divide both sides by

- 1

- u = 2 arctan (\frac{300}{319}) + 36 0^{\circ} n - 9 0^{\circ}

Divide both sides by

- 1

\frac{- u}{- 1} = \frac{2 arctan ( \frac{300}{319} )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{9 0 ^{\circ}}{- 1}

Simplify

\frac{- u}{- 1} = \frac{2 arctan ( \frac{300}{319} )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{9 0 ^{\circ}}{- 1}

Simplify

\frac{- u}{- 1} : u

\frac{- u}{- 1}

Apply the fraction rule:

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

= \frac{u}{1}

Apply rule

\frac{a}{1} = a

= u

Simplify

\frac{2 arctan ( \frac{300}{319} )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{9 0 ^{\circ}}{- 1} : - 36 0^{\circ} n + 9 0^{\circ} - 2 arctan (\frac{300}{319})

\frac{2 arctan ( \frac{300}{319} )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{9 0 ^{\circ}}{- 1}

Group like terms

= \frac{36 0 ^{\circ} n}{- 1} - \frac{9 0 ^{\circ}}{- 1} + \frac{2 arctan ( \frac{300}{319} )}{- 1}

\frac{36 0 ^{\circ} n}{- 1} = - 36 0^{\circ} n

\frac{36 0 ^{\circ} n}{- 1}

Apply the fraction rule:

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

= - \frac{36 0 ^{\circ} n}{1}

Apply rule

\frac{a}{1} = a

= - 36 0^{\circ} n

= - 36 0^{\circ} n - \frac{9 0 ^{\circ}}{- 1} + \frac{2 arctan ( \frac{300}{319} )}{- 1}

\frac{9 0 ^{\circ}}{- 1} = - 9 0^{\circ}

\frac{9 0 ^{\circ}}{- 1}

Apply the fraction rule:

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

= - \frac{9 0 ^{\circ}}{1}

Apply the fraction rule:

\frac{a}{1} = a

\frac{9 0 ^{\circ}}{1} = 9 0^{\circ}

= - 9 0^{\circ}

\frac{2 arctan ( \frac{300}{319} )}{- 1} = - 2 arctan (\frac{300}{319})

\frac{2 arctan ( \frac{300}{319} )}{- 1}

Apply the fraction rule:

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

= - \frac{2 arctan ( \frac{300}{319} )}{1}

Apply the fraction rule:

\frac{a}{1} = a

\frac{2 arctan ( \frac{300}{319} )}{1} = 2 arctan (\frac{300}{319})

= - 2 arctan (\frac{300}{319})

= - 36 0^{\circ} n - (- 9 0^{\circ}) - 2 arctan (\frac{300}{319})

Apply rule

- (- a) = a

= - 36 0^{\circ} n + 9 0^{\circ} - 2 arctan (\frac{300}{319})

u = - 36 0^{\circ} n + 9 0^{\circ} - 2 arctan (\frac{300}{319})

u = - 36 0^{\circ} n + 9 0^{\circ} - 2 arctan (\frac{300}{319})

u = - 36 0^{\circ} n + 9 0^{\circ} - 2 arctan (\frac{300}{319})

u = - 36 0^{\circ} n + 9 0^{\circ} - 2 arctan (\frac{300}{319})

Show solutions in decimal form

u = - 36 0^{\circ} n + 9 0^{\circ} - 2 \cdot 0.75471 \dots

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Frequently Asked Questions (FAQ)

What is the general solution for (12000}{2*6380}=tan(\frac{90-u)/2) ?
The general solution for (12000}{2*6380}=tan(\frac{90-u)/2) is u=-360n+90-2*0.75471…