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

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

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

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

x = \frac{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{π}{3} + πn

x = \frac{π}{3} + πn

2 sin (3 x - \frac{π}{3}) = - 3, 0 \leq x \leq 2 π

sin (x) = 2 \cdot sin (3 x)

tan^{2} (x) - 5 tan (x) - 6 = 0

tan (θ) = \frac{12}{5}

2 cos^{2} (t) = 1 - cos (t)

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