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

The general solution for tan(3x)=0 is x=(pin)/3

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tan(3x)=0

tan (3 x) = 0

x = \frac{πn}{3}

Degrees

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

Solution steps

tan (3 x) = 0

General solutions for

tan (3 x) = 0

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 = 0 + πn

3 x = 0 + πn

Solve

3 x = 0 + πn : x = \frac{πn}{3}

3 x = 0 + πn

0 + πn = πn

3 x = πn

Divide both sides by

3

3 x = πn

Divide both sides by

3

\frac{3 x}{3} = \frac{πn}{3}

Simplify

x = \frac{πn}{3}

x = \frac{πn}{3}

x = \frac{πn}{3}

2 cos^{2} (θ) = 2 - cos (2 θ)

tan (x) = 2

tan^{2} (x) + tan (x) - 20 = 0

8 cos^{2} (x) - 2 = 0

4 sin^{2} (x) tan (x) - tan (x) = 0

What is the general solution for tan(3x)=0 ?
The general solution for tan(3x)=0 is x=(pin)/3