What is the general solution for tan(x/6)+sqrt(3)=0 ?

The general solution for tan(x/6)+sqrt(3)=0 is x=4pi+6pin

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tan(x/6)+sqrt(3)=0

tan (\frac{x}{6}) + 3 = 0

x = 4 π + 6 πn

Degrees

x = 72 0^{\circ} + 108 0^{\circ} n

Solution steps

tan (\frac{x}{6}) + 3 = 0

Move

3

to the right side

tan (\frac{x}{6}) + 3 = 0

Subtract

3

from both sides

tan (\frac{x}{6}) + 3 - 3 = 0 - 3

Simplify

tan (\frac{x}{6}) = - 3

tan (\frac{x}{6}) = - 3

General solutions for

tan (\frac{x}{6}) = - 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}{6} = \frac{2 π}{3} + πn

\frac{x}{6} = \frac{2 π}{3} + πn

Solve

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

\frac{x}{6} = \frac{2 π}{3} + πn

Multiply both sides by

6

\frac{x}{6} = \frac{2 π}{3} + πn

Multiply both sides by

6

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

Simplify

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

Simplify

\frac{6 x}{6} : x

\frac{6 x}{6}

Divide the numbers:

\frac{6}{6} = 1

= x

Simplify

6 \cdot \frac{2 π}{3} + 6 πn : 4 π + 6 πn

6 \cdot \frac{2 π}{3} + 6 πn

6 \cdot \frac{2 π}{3} = 4 π

6 \cdot \frac{2 π}{3}

Multiply fractions:

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

= \frac{2 π 6}{3}

Multiply the numbers:

2 \cdot 6 = 12

= \frac{12 π}{3}

Divide the numbers:

\frac{12}{3} = 4

= 4 π

= 4 π + 6 πn

x = 4 π + 6 πn

x = 4 π + 6 πn

x = 4 π + 6 πn

x = 4 π + 6 πn

What is the general solution for tan(x/6)+sqrt(3)=0 ?
The general solution for tan(x/6)+sqrt(3)=0 is x=4pi+6pin