What is the general solution for cot(4x)=-(sqrt(3))/3 ?

The general solution for cot(4x)=-(sqrt(3))/3 is x= pi/6+(pin)/4

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cot(4x)=-(sqrt(3))/3

cot (4 x) = - \frac{3}{3}

x = \frac{π}{6} + \frac{πn}{4}

Degrees

x = 3 0^{\circ} + 4 5^{\circ} n

Solution steps

cot (4 x) = - \frac{3}{3}

General solutions for

cot (4 x) = - \frac{3}{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

4 x = \frac{2 π}{3} + πn

4 x = \frac{2 π}{3} + πn

Solve

4 x = \frac{2 π}{3} + πn : x = \frac{π}{6} + \frac{πn}{4}

4 x = \frac{2 π}{3} + πn

Divide both sides by

4

4 x = \frac{2 π}{3} + πn

Divide both sides by

4

\frac{4 x}{4} = \frac{\frac{2 π}{3}}{4} + \frac{πn}{4}

Simplify

\frac{4 x}{4} = \frac{\frac{2 π}{3}}{4} + \frac{πn}{4}

Simplify

\frac{4 x}{4} : x

\frac{4 x}{4}

Divide the numbers:

\frac{4}{4} = 1

= x

Simplify

\frac{\frac{2 π}{3}}{4} + \frac{πn}{4} : \frac{π}{6} + \frac{πn}{4}

\frac{\frac{2 π}{3}}{4} + \frac{πn}{4}

\frac{\frac{2 π}{3}}{4} = \frac{π}{6}

\frac{\frac{2 π}{3}}{4}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{2 π}{3 \cdot 4}

Multiply the numbers:

3 \cdot 4 = 12

= \frac{2 π}{12}

Cancel the common factor:

2

= \frac{π}{6}

= \frac{π}{6} + \frac{πn}{4}

x = \frac{π}{6} + \frac{πn}{4}

x = \frac{π}{6} + \frac{πn}{4}

x = \frac{π}{6} + \frac{πn}{4}

x = \frac{π}{6} + \frac{πn}{4}

sin (x) = \frac{3.9}{8.1}

5 sin (x) = - 2 cos^{2} (x) + 4

1 + cos (θ) = 1 - cos (θ)

4 cos (x) - 22 = 0

sin (x) cos (3 x) + cos (x) sin (3 x) = 0

What is the general solution for cot(4x)=-(sqrt(3))/3 ?
The general solution for cot(4x)=-(sqrt(3))/3 is x= pi/6+(pin)/4