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

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

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cot(θ)= 1/(sqrt(3))

cot (θ) = \frac{1}{3}

θ = \frac{π}{3} + πn

Solution steps

cot (θ) = \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 (θ) = \frac{3}{3}

General solutions for

cot (θ) = \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

θ = \frac{π}{3} + πn

θ = \frac{π}{3} + πn

- 3 sin^{2} (θ) + 4 sin (θ) - 7 = - 6

sin (2 x) - cos (2 x) = 1

sin (x + \frac{π}{6}) + cos (x + \frac{π}{6}) = 1

sin (x) = - 1, 0 \leq x \leq 2 π

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

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