What is the general solution for cot((-x+3n)/4)=0 ?

The general solution for cot((-x+3n)/4)=0 is x=-2pi-4pik+3n

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cot((-x+3n)/4)=0

Solution

cot (\frac{- x + 3 n}{4}) = 0

Solution

x = - 2 π - 4 πk + 3 n

Solution steps

cot (\frac{- x + 3 n}{4}) = 0

General solutions for

cot (\frac{- x + 3 n}{4}) = 0

cot (x)

periodicity table with

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} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

\frac{- x + 3 n}{4} = \frac{π}{2} + πn

\frac{- x + 3 n}{4} = \frac{π}{2} + πn

Solve

\frac{- x + 3 n}{4} = \frac{π}{2} + πk : x = - 2 π - 4 πk + 3 n

\frac{- x + 3 n}{4} = \frac{π}{2} + πk

Multiply both sides by

4

\frac{- x + 3 n}{4} = \frac{π}{2} + πk

Multiply both sides by

4

\frac{4 ( - x + 3 n )}{4} = 4 \cdot \frac{π}{2} + 4 πk

Simplify

\frac{4 ( - x + 3 n )}{4} = 4 \cdot \frac{π}{2} + 4 πk

Simplify

\frac{4 ( - x + 3 n )}{4} : - x + 3 n

\frac{4 ( - x + 3 n )}{4}

Divide the numbers:

\frac{4}{4} = 1

= - x + 3 n

Simplify

4 \cdot \frac{π}{2} + 4 πk : 2 π + 4 πk

4 \cdot \frac{π}{2} + 4 πk

4 \cdot \frac{π}{2} = 2 π

4 \cdot \frac{π}{2}

Multiply fractions:

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

= \frac{π 4}{2}

Divide the numbers:

\frac{4}{2} = 2

= 2 π

= 2 π + 4 πk

- x + 3 n = 2 π + 4 πk

- x + 3 n = 2 π + 4 πk

- x + 3 n = 2 π + 4 πk

Move

3 n

to the right side

- x + 3 n = 2 π + 4 πk

Subtract

3 n

from both sides

- x + 3 n - 3 n = 2 π + 4 πk - 3 n

Simplify

- x = 2 π + 4 πk - 3 n

- x = 2 π + 4 πk - 3 n

Divide both sides by

- 1

- x = 2 π + 4 πk - 3 n

Divide both sides by

- 1

\frac{- x}{- 1} = \frac{2 π}{- 1} + \frac{4 πk}{- 1} - \frac{3 n}{- 1}

Simplify

\frac{- x}{- 1} = \frac{2 π}{- 1} + \frac{4 πk}{- 1} - \frac{3 n}{- 1}

Simplify

\frac{- x}{- 1} : x

\frac{- x}{- 1}

Apply the fraction rule:

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

= \frac{x}{1}

Apply rule

\frac{a}{1} = a

= x

Simplify

\frac{2 π}{- 1} + \frac{4 πk}{- 1} - \frac{3 n}{- 1} : - 2 π - 4 πk + 3 n

\frac{2 π}{- 1} + \frac{4 πk}{- 1} - \frac{3 n}{- 1}

\frac{2 π}{- 1} = - 2 π

\frac{2 π}{- 1}

Apply the fraction rule:

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

= - \frac{2 π}{1}

Apply rule

\frac{a}{1} = a

= - 2 π

= - 2 π + \frac{4 πk}{- 1} - \frac{3 n}{- 1}

\frac{4 πk}{- 1} = - 4 πk

\frac{4 πk}{- 1}

Apply the fraction rule:

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

= - \frac{4 πk}{1}

Apply rule

\frac{a}{1} = a

= - 4 πk

= - 2 π - 4 πk - \frac{3 n}{- 1}

\frac{3 n}{- 1} = - 3 n

\frac{3 n}{- 1}

Apply the fraction rule:

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

= - \frac{3 n}{1}

Apply rule

\frac{a}{1} = a

= - 3 n

= - 2 π - 4 πk - (- 3 n)

Apply rule

- (- a) = a

= - 2 π - 4 πk + 3 n

x = - 2 π - 4 πk + 3 n

x = - 2 π - 4 πk + 3 n

x = - 2 π - 4 πk + 3 n

x = - 2 π - 4 πk + 3 n

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Frequently Asked Questions (FAQ)

What is the general solution for cot((-x+3n)/4)=0 ?
The general solution for cot((-x+3n)/4)=0 is x=-2pi-4pik+3n