What is the general solution for tan(x/9)+sqrt(3)=0 ?

The general solution for tan(x/9)+sqrt(3)=0 is x=6pi+9pin

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tan(x/9)+sqrt(3)=0

tan (\frac{x}{9}) + 3 = 0

x = 6 π + 9 πn

Degrees

x = 108 0^{\circ} + 162 0^{\circ} n

Solution steps

tan (\frac{x}{9}) + 3 = 0

Move

3

to the right side

tan (\frac{x}{9}) + 3 = 0

Subtract

3

from both sides

tan (\frac{x}{9}) + 3 - 3 = 0 - 3

Simplify

tan (\frac{x}{9}) = - 3

tan (\frac{x}{9}) = - 3

General solutions for

tan (\frac{x}{9}) = - 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}{9} = \frac{2 π}{3} + πn

\frac{x}{9} = \frac{2 π}{3} + πn

Solve

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

\frac{x}{9} = \frac{2 π}{3} + πn

Multiply both sides by

9

\frac{x}{9} = \frac{2 π}{3} + πn

Multiply both sides by

9

\frac{9 x}{9} = 9 \cdot \frac{2 π}{3} + 9 πn

Simplify

\frac{9 x}{9} = 9 \cdot \frac{2 π}{3} + 9 πn

Simplify

\frac{9 x}{9} : x

\frac{9 x}{9}

Divide the numbers:

\frac{9}{9} = 1

= x

Simplify

9 \cdot \frac{2 π}{3} + 9 πn : 6 π + 9 πn

9 \cdot \frac{2 π}{3} + 9 πn

9 \cdot \frac{2 π}{3} = 6 π

9 \cdot \frac{2 π}{3}

Multiply fractions:

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

= \frac{2 π 9}{3}

Multiply the numbers:

2 \cdot 9 = 18

= \frac{18 π}{3}

Divide the numbers:

\frac{18}{3} = 6

= 6 π

= 6 π + 9 πn

x = 6 π + 9 πn

x = 6 π + 9 πn

x = 6 π + 9 πn

x = 6 π + 9 πn

What is the general solution for tan(x/9)+sqrt(3)=0 ?
The general solution for tan(x/9)+sqrt(3)=0 is x=6pi+9pin