What is the general solution for 3cot(x)+4=7 ?

The general solution for 3cot(x)+4=7 is x= pi/4+pin

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3cot(x)+4=7

3 cot (x) + 4 = 7

x = \frac{π}{4} + πn

Degrees

x = 4 5^{\circ} + 18 0^{\circ} n

Solution steps

3 cot (x) + 4 = 7

Move

4

to the right side

3 cot (x) + 4 = 7

Subtract

4

from both sides

3 cot (x) + 4 - 4 = 7 - 4

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) = 1

cot (x) = 1

General solutions for

cot (x) = 1

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{π}{4} + πn

x = \frac{π}{4} + πn

What is the general solution for 3cot(x)+4=7 ?
The general solution for 3cot(x)+4=7 is x= pi/4+pin