What is the general solution for sqrt(3)tan(x/4)+5=4 ?

The general solution for sqrt(3)tan(x/4)+5=4 is x=(10pi)/3+4pin

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Popular Trigonometry >

sqrt(3)tan(x/4)+5=4

Solution

3 tan (\frac{x}{4}) + 5 = 4

Solution

x = \frac{10 π}{3} + 4 πn

Degrees

x = 60 0^{\circ} + 72 0^{\circ} n

Solution steps

3 tan (\frac{x}{4}) + 5 = 4

Move

5

to the right side

3 tan (\frac{x}{4}) + 5 = 4

Subtract

5

from both sides

3 tan (\frac{x}{4}) + 5 - 5 = 4 - 5

Simplify

3 tan (\frac{x}{4}) = - 1

3 tan (\frac{x}{4}) = - 1

Divide both sides by

3

3 tan (\frac{x}{4}) = - 1

Divide both sides by

3

\frac{3 tan ( \frac{x}{4} )}{3} = \frac{- 1}{3}

Simplify

\frac{3 tan ( \frac{x}{4} )}{3} = \frac{- 1}{3}

Simplify

\frac{3 tan ( \frac{x}{4} )}{3} : tan (\frac{x}{4})

\frac{3 tan ( \frac{x}{4} )}{3}

Cancel the common factor:

3

= tan (\frac{x}{4})

Simplify

\frac{- 1}{3} : - \frac{3}{3}

\frac{- 1}{3}

Apply the fraction rule:

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

= - \frac{1}{3}

Rationalize

- \frac{1}{3} : - \frac{3}{3}

- \frac{1}{3}

Multiply by the conjugate

\frac{3}{3}

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

1 \cdot 3 = 3

33 = 3

33

Apply radical rule:

a a = a

33 = 3

= 3

= - \frac{3}{3}

= - \frac{3}{3}

tan (\frac{x}{4}) = - \frac{3}{3}

tan (\frac{x}{4}) = - \frac{3}{3}

tan (\frac{x}{4}) = - \frac{3}{3}

General solutions for

tan (\frac{x}{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{x}{4} = \frac{5 π}{6} + πn

\frac{x}{4} = \frac{5 π}{6} + πn

Solve

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

\frac{x}{4} = \frac{5 π}{6} + πn

Multiply both sides by

4

\frac{x}{4} = \frac{5 π}{6} + πn

Multiply both sides by

4

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

Simplify

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

Simplify

\frac{4 x}{4} : x

\frac{4 x}{4}

Divide the numbers:

\frac{4}{4} = 1

= x

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

x = \frac{10 π}{3} + 4 πn

x = \frac{10 π}{3} + 4 πn

x = \frac{10 π}{3} + 4 πn

x = \frac{10 π}{3} + 4 πn

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for sqrt(3)tan(x/4)+5=4 ?
The general solution for sqrt(3)tan(x/4)+5=4 is x=(10pi)/3+4pin