What is the general solution for cot((2x)/3)=-sqrt(3) ?

The general solution for cot((2x)/3)=-sqrt(3) is x=(5pi)/4+(3pin)/2

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cot((2x)/3)=-sqrt(3)

Solution

cot (\frac{2 x}{3}) = - 3

Solution

x = \frac{5 π}{4} + \frac{3 πn}{2}

Degrees

x = 22 5^{\circ} + 27 0^{\circ} n

Solution steps

cot (\frac{2 x}{3}) = - 3

General solutions for

cot (\frac{2 x}{3}) = - 3

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{2 x}{3} = \frac{5 π}{6} + πn

\frac{2 x}{3} = \frac{5 π}{6} + πn

Solve

\frac{2 x}{3} = \frac{5 π}{6} + πn : x = \frac{5 π}{4} + \frac{3 πn}{2}

\frac{2 x}{3} = \frac{5 π}{6} + πn

Multiply both sides by

3

\frac{2 x}{3} = \frac{5 π}{6} + πn

Multiply both sides by

3

\frac{3 \cdot 2 x}{3} = 3 \cdot \frac{5 π}{6} + 3 πn

Simplify

\frac{3 \cdot 2 x}{3} = 3 \cdot \frac{5 π}{6} + 3 πn

Simplify

\frac{3 \cdot 2 x}{3} : 2 x

\frac{3 \cdot 2 x}{3}

Multiply the numbers:

3 \cdot 2 = 6

= \frac{6 x}{3}

Divide the numbers:

\frac{6}{3} = 2

= 2 x

Simplify

3 \cdot \frac{5 π}{6} + 3 πn : \frac{5 π}{2} + 3 πn

3 \cdot \frac{5 π}{6} + 3 πn

3 \cdot \frac{5 π}{6} = \frac{5 π}{2}

3 \cdot \frac{5 π}{6}

Multiply fractions:

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

= \frac{5 π 3}{6}

Multiply the numbers:

5 \cdot 3 = 15

= \frac{15 π}{6}

Cancel the common factor:

3

= \frac{5 π}{2}

= \frac{5 π}{2} + 3 πn

2 x = \frac{5 π}{2} + 3 πn

2 x = \frac{5 π}{2} + 3 πn

2 x = \frac{5 π}{2} + 3 πn

Divide both sides by

2

2 x = \frac{5 π}{2} + 3 πn

Divide both sides by

2

\frac{2 x}{2} = \frac{\frac{5 π}{2}}{2} + \frac{3 πn}{2}

Simplify

\frac{2 x}{2} = \frac{\frac{5 π}{2}}{2} + \frac{3 πn}{2}

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

\frac{\frac{5 π}{2}}{2} + \frac{3 πn}{2} : \frac{5 π}{4} + \frac{3 πn}{2}

\frac{\frac{5 π}{2}}{2} + \frac{3 πn}{2}

\frac{\frac{5 π}{2}}{2} = \frac{5 π}{4}

\frac{\frac{5 π}{2}}{2}

Apply the fraction rule:

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

= \frac{5 π}{2 \cdot 2}

Multiply the numbers:

2 \cdot 2 = 4

= \frac{5 π}{4}

= \frac{5 π}{4} + \frac{3 πn}{2}

x = \frac{5 π}{4} + \frac{3 πn}{2}

x = \frac{5 π}{4} + \frac{3 πn}{2}

x = \frac{5 π}{4} + \frac{3 πn}{2}

x = \frac{5 π}{4} + \frac{3 πn}{2}

Popular Examples

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Frequently Asked Questions (FAQ)

What is the general solution for cot((2x)/3)=-sqrt(3) ?
The general solution for cot((2x)/3)=-sqrt(3) is x=(5pi)/4+(3pin)/2