What is the general solution for tan(4θ)=0 ?

The general solution for tan(4θ)=0 is θ=(pin)/4

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tan(4θ)=0

tan (4 θ) = 0

θ = \frac{πn}{4}

Degrees

θ = 0^{\circ} + 4 5^{\circ} n

Solution steps

tan (4 θ) = 0

General solutions for

tan (4 θ) = 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}

4 θ = 0 + πn

4 θ = 0 + πn

Solve

4 θ = 0 + πn : θ = \frac{πn}{4}

4 θ = 0 + πn

0 + πn = πn

4 θ = πn

Divide both sides by

4

4 θ = πn

Divide both sides by

4

\frac{4 θ}{4} = \frac{πn}{4}

Simplify

θ = \frac{πn}{4}

θ = \frac{πn}{4}

θ = \frac{πn}{4}

What is the general solution for tan(4θ)=0 ?
The general solution for tan(4θ)=0 is θ=(pin)/4