What is the general solution for tan(5x)=0 ?

The general solution for tan(5x)=0 is x=(pin)/5

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tan(5x)=0

tan (5 x) = 0

x = \frac{πn}{5}

Degrees

x = 0^{\circ} + 3 6^{\circ} n

Solution steps

tan (5 x) = 0

General solutions for

tan (5 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}

5 x = 0 + πn

5 x = 0 + πn

Solve

5 x = 0 + πn : x = \frac{πn}{5}

5 x = 0 + πn

0 + πn = πn

5 x = πn

Divide both sides by

5

5 x = πn

Divide both sides by

5

\frac{5 x}{5} = \frac{πn}{5}

Simplify

x = \frac{πn}{5}

x = \frac{πn}{5}

x = \frac{πn}{5}

4 cos^{2} (θ) - 2 = 0

3 cos (2 θ) - 4 sin (θ) + 2 = sin (θ) + 6

2 cos (x) sin (x) + cos (x) = 0

6 cos (x) - 6 sin (x) = 36

cos^{2} (θ) + cos^{4} (θ) = 1

What is the general solution for tan(5x)=0 ?
The general solution for tan(5x)=0 is x=(pin)/5