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

The general solution for tan(3x)+sqrt(3)=0 is x=(2pi)/9+(pin)/3

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

tan (3 x) + 3 = 0

x = \frac{2 π}{9} + \frac{πn}{3}

Degrees

x = 4 0^{\circ} + 6 0^{\circ} n

Solution steps

tan (3 x) + 3 = 0

Move

3

to the right side

tan (3 x) + 3 = 0

Subtract

3

from both sides

tan (3 x) + 3 - 3 = 0 - 3

Simplify

tan (3 x) = - 3

tan (3 x) = - 3

General solutions for

tan (3 x) = - 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}

3 x = \frac{2 π}{3} + πn

3 x = \frac{2 π}{3} + πn

Solve

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

3 x = \frac{2 π}{3} + πn

Divide both sides by

3

3 x = \frac{2 π}{3} + πn

Divide both sides by

3

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

Simplify

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

Simplify

\frac{3 x}{3} : x

\frac{3 x}{3}

Divide the numbers:

\frac{3}{3} = 1

= x

Simplify

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

\frac{\frac{2 π}{3}}{3} + \frac{πn}{3}

\frac{\frac{2 π}{3}}{3} = \frac{2 π}{9}

\frac{\frac{2 π}{3}}{3}

Apply the fraction rule:

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

= \frac{2 π}{3 \cdot 3}

Multiply the numbers:

3 \cdot 3 = 9

= \frac{2 π}{9}

= \frac{2 π}{9} + \frac{πn}{3}

x = \frac{2 π}{9} + \frac{πn}{3}

x = \frac{2 π}{9} + \frac{πn}{3}

x = \frac{2 π}{9} + \frac{πn}{3}

x = \frac{2 π}{9} + \frac{πn}{3}

sin (θ) = \frac{2 2}{3}

cos (θ) = \frac{1}{2}

cos (3 x) = sin (3 x)

sin (t) = \frac{3}{5}

cos (2 x) + 5 cos (x) = 2

What is the general solution for tan(3x)+sqrt(3)=0 ?
The general solution for tan(3x)+sqrt(3)=0 is x=(2pi)/9+(pin)/3