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

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

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3cot(θ)=-sqrt(3)

3 cot (θ) = - 3

θ = \frac{2 π}{3} + πn

Degrees

θ = 12 0^{\circ} + 18 0^{\circ} n

Solution steps

3 cot (θ) = - 3

Divide both sides by

3

3 cot (θ) = - 3

Divide both sides by

3

\frac{3 cot ( θ )}{3} = \frac{- 3}{3}

Simplify

cot (θ) = - \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{2 π}{3} + πn

θ = \frac{2 π}{3} + πn

tan (2 x) = \frac{2}{3}

sin^{2} (x) = 1 - cos (2 x)

sin (θ) = \frac{5}{6}, cos (θ)

tan^{2} (t) - sec^{2} (t) = 1

sin (x) tan (x) = \frac{1}{cot ( x )}

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