What is the general solution for tan((3θ)/4)=(-sqrt(3))/3 ?

The general solution for tan((3θ)/4)=(-sqrt(3))/3 is θ=(10pi)/9+(4pin)/3

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Popular Trigonometry >

tan((3θ)/4)=(-sqrt(3))/3

Solution

tan (\frac{3 θ}{4}) = \frac{- 3}{3}

Solution

θ = \frac{10 π}{9} + \frac{4 πn}{3}

Degrees

θ = 20 0^{\circ} + 24 0^{\circ} n

Solution steps

tan (\frac{3 θ}{4}) = \frac{- 3}{3}

Apply the fraction rule:

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

tan (\frac{3 θ}{4}) = - \frac{3}{3}

General solutions for

tan (\frac{3 θ}{4}) = - \frac{3}{3}

tan (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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

\frac{3 θ}{4} = \frac{5 π}{6} + πn

\frac{3 θ}{4} = \frac{5 π}{6} + πn

Solve

\frac{3 θ}{4} = \frac{5 π}{6} + πn : θ = \frac{10 π}{9} + \frac{4 πn}{3}

\frac{3 θ}{4} = \frac{5 π}{6} + πn

Multiply both sides by

4

\frac{3 θ}{4} = \frac{5 π}{6} + πn

Multiply both sides by

4

\frac{4 \cdot 3 θ}{4} = 4 \cdot \frac{5 π}{6} + 4 πn

Simplify

\frac{4 \cdot 3 θ}{4} = 4 \cdot \frac{5 π}{6} + 4 πn

Simplify

\frac{4 \cdot 3 θ}{4} : 3 θ

\frac{4 \cdot 3 θ}{4}

Multiply the numbers:

4 \cdot 3 = 12

= \frac{12 θ}{4}

Divide the numbers:

\frac{12}{4} = 3

= 3 θ

Simplify

4 \cdot \frac{5 π}{6} + 4 πn : \frac{10 π}{3} + 4 πn

4 \cdot \frac{5 π}{6} + 4 πn

4 \cdot \frac{5 π}{6} = \frac{10 π}{3}

4 \cdot \frac{5 π}{6}

Multiply fractions:

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

= \frac{5 π 4}{6}

Multiply the numbers:

5 \cdot 4 = 20

= \frac{20 π}{6}

Cancel the common factor:

2

= \frac{10 π}{3}

= \frac{10 π}{3} + 4 πn

3 θ = \frac{10 π}{3} + 4 πn

3 θ = \frac{10 π}{3} + 4 πn

3 θ = \frac{10 π}{3} + 4 πn

Divide both sides by

3

3 θ = \frac{10 π}{3} + 4 πn

Divide both sides by

3

\frac{3 θ}{3} = \frac{\frac{10 π}{3}}{3} + \frac{4 πn}{3}

Simplify

\frac{3 θ}{3} = \frac{\frac{10 π}{3}}{3} + \frac{4 πn}{3}

Simplify

\frac{3 θ}{3} : θ

\frac{3 θ}{3}

Divide the numbers:

\frac{3}{3} = 1

= θ

Simplify

\frac{\frac{10 π}{3}}{3} + \frac{4 πn}{3} : \frac{10 π}{9} + \frac{4 πn}{3}

\frac{\frac{10 π}{3}}{3} + \frac{4 πn}{3}

\frac{\frac{10 π}{3}}{3} = \frac{10 π}{9}

\frac{\frac{10 π}{3}}{3}

Apply the fraction rule:

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

= \frac{10 π}{3 \cdot 3}

Multiply the numbers:

3 \cdot 3 = 9

= \frac{10 π}{9}

= \frac{10 π}{9} + \frac{4 πn}{3}

θ = \frac{10 π}{9} + \frac{4 πn}{3}

θ = \frac{10 π}{9} + \frac{4 πn}{3}

θ = \frac{10 π}{9} + \frac{4 πn}{3}

θ = \frac{10 π}{9} + \frac{4 πn}{3}

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for tan((3θ)/4)=(-sqrt(3))/3 ?
The general solution for tan((3θ)/4)=(-sqrt(3))/3 is θ=(10pi)/9+(4pin)/3