What is the general solution for 3cot(x-2)+sqrt(3)=0 ?

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

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3cot(x-2)+sqrt(3)=0

3 cot (x - 2) + 3 = 0

x = \frac{2 π}{3} + πn + 2

Degrees

x = 234.59155 \dots^{\circ} + 18 0^{\circ} n

Solution steps

3 cot (x - 2) + 3 = 0

Move

3

to the right side

3 cot (x - 2) + 3 = 0

Subtract

3

from both sides

3 cot (x - 2) + 3 - 3 = 0 - 3

Simplify

3 cot (x - 2) = - 3

3 cot (x - 2) = - 3

Divide both sides by

3

3 cot (x - 2) = - 3

Divide both sides by

3

\frac{3 cot ( x - 2 )}{3} = \frac{- 3}{3}

Simplify

cot (x - 2) = - \frac{3}{3}

cot (x - 2) = - \frac{3}{3}

General solutions for

cot (x - 2) = - \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 - 2 = \frac{2 π}{3} + πn

x - 2 = \frac{2 π}{3} + πn

Solve

x - 2 = \frac{2 π}{3} + πn : x = \frac{2 π}{3} + πn + 2

x - 2 = \frac{2 π}{3} + πn

Move

2

to the right side

x - 2 = \frac{2 π}{3} + πn

Add

2

to both sides

x - 2 + 2 = \frac{2 π}{3} + πn + 2

Simplify

x = \frac{2 π}{3} + πn + 2

x = \frac{2 π}{3} + πn + 2

x = \frac{2 π}{3} + πn + 2

sin (2 x) + 3 sin (4 x) = 0

- 2 sin^{2} (3 x) = cos (3 x) - 2

2 sin^{2} (θ) = cos (θ) + 1

arccsc (2 x) + arcsin (0) = arctan (\frac{1}{3})

sin (t) + cos (2 t) = 0.75

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