What is the general solution for 3tan(x/3)+sqrt(3)=0 ?

The general solution for 3tan(x/3)+sqrt(3)=0 is x=(5pi)/2+3pin

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Popular >

3tan(x/3)+sqrt(3)=0

Solution

3 tan (\frac{x}{3}) + 3 = 0

Solution

x = \frac{5 π}{2} + 3 πn

Degrees

x = 45 0^{\circ} + 54 0^{\circ} n

Solution steps

3 tan (\frac{x}{3}) + 3 = 0

Move

3

to the right side

3 tan (\frac{x}{3}) + 3 = 0

Subtract

3

from both sides

3 tan (\frac{x}{3}) + 3 - 3 = 0 - 3

Simplify

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

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

Divide both sides by

3

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

Divide both sides by

3

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

Simplify

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

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

General solutions for

tan (\frac{x}{3}) = - \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}{3} = \frac{5 π}{6} + πn

\frac{x}{3} = \frac{5 π}{6} + πn

Solve

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

\frac{x}{3} = \frac{5 π}{6} + πn

Multiply both sides by

3

\frac{x}{3} = \frac{5 π}{6} + πn

Multiply both sides by

3

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

Simplify

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

Simplify

\frac{3 x}{3} : x

\frac{3 x}{3}

Divide the numbers:

\frac{3}{3} = 1

= 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

x = \frac{5 π}{2} + 3 πn

x = \frac{5 π}{2} + 3 πn

x = \frac{5 π}{2} + 3 πn

x = \frac{5 π}{2} + 3 πn

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Frequently Asked Questions (FAQ)

What is the general solution for 3tan(x/3)+sqrt(3)=0 ?
The general solution for 3tan(x/3)+sqrt(3)=0 is x=(5pi)/2+3pin