What is the general solution for cot(3θ)=sqrt(3) ?

The general solution for cot(3θ)=sqrt(3) is θ= pi/(18)+(pin)/3

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cot(3θ)=sqrt(3)

cot (3 θ) = 3

θ = \frac{π}{18} + \frac{πn}{3}

Degrees

θ = 1 0^{\circ} + 6 0^{\circ} n

Solution steps

cot (3 θ) = 3

General solutions for

cot (3 θ) = 3

cot (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} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

3 θ = \frac{π}{6} + πn

3 θ = \frac{π}{6} + πn

Solve

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

3 θ = \frac{π}{6} + πn

Divide both sides by

3

3 θ = \frac{π}{6} + πn

Divide both sides by

3

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

Simplify

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

Simplify

\frac{3 θ}{3} : θ

\frac{3 θ}{3}

Divide the numbers:

\frac{3}{3} = 1

= θ

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}

θ = \frac{π}{18} + \frac{πn}{3}

θ = \frac{π}{18} + \frac{πn}{3}

θ = \frac{π}{18} + \frac{πn}{3}

θ = \frac{π}{18} + \frac{πn}{3}

tan (x) = \frac{45}{35}

3 (2 sin (x) - 2) \cdot (4 cos (x) - 2) = 0

0 = \frac{1}{3} \cdot cot (- 4 θ)

\frac{62 5 ^{c o s^{2} (x)}}{2 5 ^{c o s (x)}} = 1

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

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