What is the general solution for tan((2x)/3)=0 ?

The general solution for tan((2x)/3)=0 is x=(3pin)/2

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tan((2x)/3)=0

tan (\frac{2 x}{3}) = 0

x = \frac{3 πn}{2}

Degrees

x = 0^{\circ} + 27 0^{\circ} n

Solution steps

tan (\frac{2 x}{3}) = 0

General solutions for

tan (\frac{2 x}{3}) = 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}

\frac{2 x}{3} = 0 + πn

\frac{2 x}{3} = 0 + πn

Solve

\frac{2 x}{3} = 0 + πn : x = \frac{3 πn}{2}

\frac{2 x}{3} = 0 + πn

0 + πn = πn

\frac{2 x}{3} = πn

Multiply both sides by

3

\frac{2 x}{3} = πn

Multiply both sides by

3

\frac{3 \cdot 2 x}{3} = 3 πn

Simplify

2 x = 3 πn

2 x = 3 πn

Divide both sides by

2

2 x = 3 πn

Divide both sides by

2

\frac{2 x}{2} = \frac{3 πn}{2}

Simplify

x = \frac{3 πn}{2}

x = \frac{3 πn}{2}

x = \frac{3 πn}{2}

3 cos^{2} (A) + 3 cos (A) = 0

3 csc (2 x) - 2 = 0

cos (3 x) (2 cos (x) + 1) = 0

3 csc (θ) - 1 = 0

5 sin (x) tan (x) - 10 tan (x) + 3 sin (x) - 6 = 0

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