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

The general solution for cot(x)+sqrt(3)=0 is x=(5pi)/6+pin

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cot(x)+sqrt(3)=0

cot (x) + 3 = 0

x = \frac{5 π}{6} + πn

Degrees

x = 15 0^{\circ} + 18 0^{\circ} n

Solution steps

cot (x) + 3 = 0

Move

3

to the right side

cot (x) + 3 = 0

Subtract

3

from both sides

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

Simplify

cot (x) = - 3

cot (x) = - 3

General solutions for

cot (x) = - 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{5 π}{6} + πn

x = \frac{5 π}{6} + πn

4 sin^{2} (θ) + 4 = 5

sec^{2} (x) - 6 tan (x) = - 4

64 cos^{2} (x) - 16 = 0

\frac{1}{2} cos (\frac{x}{2}) = 0

cos (2 x) = - \frac{2}{2}

What is the general solution for cot(x)+sqrt(3)=0 ?
The general solution for cot(x)+sqrt(3)=0 is x=(5pi)/6+pin