What is the general solution for cot(x)=-1/(sqrt(3)) ?

The general solution for cot(x)=-1/(sqrt(3)) is x=(2pi)/3+pin

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cot(x)=-1/(sqrt(3))

cot (x) = - \frac{1}{3}

x = \frac{2 π}{3} + πn

Solution steps

cot (x) = - \frac{1}{3}

Simplify

- \frac{1}{3} : - \frac{3}{3}

- \frac{1}{3}

Multiply by the conjugate

\frac{3}{3}

= - \frac{1 \cdot 3}{3 3}

1 \cdot 3 = 3

33 = 3

33

Apply radical rule:

a a = a

33 = 3

= 3

= - \frac{3}{3}

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

General solutions for

cot (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

x = \frac{2 π}{3} + πn

x = \frac{2 π}{3} + πn

4 cos^{2} (x) + 2 cos (x) - 2 = 0

tan (3 x) = 0

2 cos^{2} (θ) = 2 - cos (2 θ)

tan (x) = 2

tan^{2} (x) + tan (x) - 20 = 0

What is the general solution for cot(x)=-1/(sqrt(3)) ?
The general solution for cot(x)=-1/(sqrt(3)) is x=(2pi)/3+pin