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

The general solution for cot((3θ)/2)=-sqrt(3) is θ=(5pi)/9+(2pin)/3

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cot((3θ)/2)=-sqrt(3)

Solution

cot (\frac{3 θ}{2}) = - 3

Solution

θ = \frac{5 π}{9} + \frac{2 πn}{3}

Degrees

θ = 10 0^{\circ} + 12 0^{\circ} n

Solution steps

cot (\frac{3 θ}{2}) = - 3

General solutions for

cot (\frac{3 θ}{2}) = - 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{3 θ}{2} = \frac{5 π}{6} + πn

\frac{3 θ}{2} = \frac{5 π}{6} + πn

Solve

\frac{3 θ}{2} = \frac{5 π}{6} + πn : θ = \frac{5 π}{9} + \frac{2 πn}{3}

\frac{3 θ}{2} = \frac{5 π}{6} + πn

Multiply both sides by

2

\frac{3 θ}{2} = \frac{5 π}{6} + πn

Multiply both sides by

2

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

Simplify

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

Simplify

\frac{2 \cdot 3 θ}{2} : 3 θ

\frac{2 \cdot 3 θ}{2}

Multiply the numbers:

2 \cdot 3 = 6

= \frac{6 θ}{2}

Divide the numbers:

\frac{6}{2} = 3

= 3 θ

Simplify

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

2 \cdot \frac{5 π}{6} + 2 πn

2 \cdot \frac{5 π}{6} = \frac{5 π}{3}

2 \cdot \frac{5 π}{6}

Multiply fractions:

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

= \frac{5 π 2}{6}

Multiply the numbers:

5 \cdot 2 = 10

= \frac{10 π}{6}

Cancel the common factor:

2

= \frac{5 π}{3}

= \frac{5 π}{3} + 2 πn

3 θ = \frac{5 π}{3} + 2 πn

3 θ = \frac{5 π}{3} + 2 πn

3 θ = \frac{5 π}{3} + 2 πn

Divide both sides by

3

3 θ = \frac{5 π}{3} + 2 πn

Divide both sides by

3

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

Simplify

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

Simplify

\frac{3 θ}{3} : θ

\frac{3 θ}{3}

Divide the numbers:

\frac{3}{3} = 1

= θ

Simplify

\frac{\frac{5 π}{3}}{3} + \frac{2 πn}{3} : \frac{5 π}{9} + \frac{2 πn}{3}

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

\frac{\frac{5 π}{3}}{3} = \frac{5 π}{9}

\frac{\frac{5 π}{3}}{3}

Apply the fraction rule:

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

= \frac{5 π}{3 \cdot 3}

Multiply the numbers:

3 \cdot 3 = 9

= \frac{5 π}{9}

= \frac{5 π}{9} + \frac{2 πn}{3}

θ = \frac{5 π}{9} + \frac{2 πn}{3}

θ = \frac{5 π}{9} + \frac{2 πn}{3}

θ = \frac{5 π}{9} + \frac{2 πn}{3}

θ = \frac{5 π}{9} + \frac{2 πn}{3}

Popular Examples

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sin^{2} (2 x) - sin (2 x) - 2 = 0

tan^2(x)-3sec(x)=-3

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2sin(1/2 x)-sqrt(2)=0

2 sin (\frac{1}{2} x) - 2 = 0

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11 sin (b) - 1 = 3 sin (b) - 1

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Frequently Asked Questions (FAQ)

What is the general solution for cot((3θ)/2)=-sqrt(3) ?
The general solution for cot((3θ)/2)=-sqrt(3) is θ=(5pi)/9+(2pin)/3