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

The general solution for tan(3x)=(sqrt(3))/3 is x= pi/(18)+(pin)/3

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

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

x = \frac{π}{18} + \frac{πn}{3}

Degrees

x = 1 0^{\circ} + 6 0^{\circ} n

Solution steps

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

General solutions for

tan (3 x) = \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}

3 x = \frac{π}{6} + πn

3 x = \frac{π}{6} + πn

Solve

3 x = \frac{π}{6} + πn : x = \frac{π}{18} + \frac{πn}{3}

3 x = \frac{π}{6} + πn

Divide both sides by

3

3 x = \frac{π}{6} + πn

Divide both sides by

3

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

Simplify

\frac{3 x}{3} = \frac{\frac{π}{6}}{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{π}{6}}{3} + \frac{πn}{3} : \frac{π}{18} + \frac{πn}{3}

\frac{\frac{π}{6}}{3} + \frac{πn}{3}

\frac{\frac{π}{6}}{3} = \frac{π}{18}

\frac{\frac{π}{6}}{3}

Apply the fraction rule:

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

= \frac{π}{6 \cdot 3}

Multiply the numbers:

6 \cdot 3 = 18

= \frac{π}{18}

= \frac{π}{18} + \frac{πn}{3}

x = \frac{π}{18} + \frac{πn}{3}

x = \frac{π}{18} + \frac{πn}{3}

x = \frac{π}{18} + \frac{πn}{3}

x = \frac{π}{18} + \frac{πn}{3}

sin (x) tan (x) = sin (x)

2 cos^{2} (x) + cos (2 x) = 0

9 cos^{2} (θ) - 4 = 0

sec (θ) = \frac{2 3}{3}

sin (x + \frac{π}{4}) - sin (x - \frac{5 π}{4}) = \frac{2}{2}

What is the general solution for tan(3x)=(sqrt(3))/3 ?
The general solution for tan(3x)=(sqrt(3))/3 is x= pi/(18)+(pin)/3