What is the general solution for 3cot(x)+sqrt(3)=0 ?

The general solution for 3cot(x)+sqrt(3)=0 is x=(2pi)/3+pin

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3cot(x)+sqrt(3)=0

3 cot (x) + 3 = 0

x = \frac{2 π}{3} + πn

Degrees

x = 12 0^{\circ} + 18 0^{\circ} n

Solution steps

3 cot (x) + 3 = 0

Move

3

to the right side

3 cot (x) + 3 = 0

Subtract

3

from both sides

3 cot (x) + 3 - 3 = 0 - 3

Simplify

3 cot (x) = - 3

3 cot (x) = - 3

Divide both sides by

3

3 cot (x) = - 3

Divide both sides by

3

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

Simplify

cot (x) = - \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

3 cos (x) + \frac{9}{2} = 5 + 4 cos (x)

sec (2 x) + 2 = 0

3 sin (x + 2 0^{\circ}) - 0.75 = 0

2 sin^{2} (x) + sin (x) - 5 = 0

- 4 sin (x) = 4 (sin (x) - 1)

What is the general solution for 3cot(x)+sqrt(3)=0 ?
The general solution for 3cot(x)+sqrt(3)=0 is x=(2pi)/3+pin