What is the general solution for cot(3x-6)=(sqrt(3))/3 ?

The general solution for cot(3x-6)=(sqrt(3))/3 is x=(180n)/3+22

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cot(3x-6)=(sqrt(3))/3

Solution

cot (3 x - 6^{\circ}) = \frac{3}{3}

Solution

x = \frac{18 0 ^{\circ} n}{3} + 2 2^{\circ}

Radians

x = \frac{11 π}{90} + \frac{π}{3} n

Solution steps

cot (3 x - 6^{\circ}) = \frac{3}{3}

General solutions for

cot (3 x - 6^{\circ}) = \frac{3}{3}

cot (x)

periodicity table with

18 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

3 x - 6^{\circ} = 6 0^{\circ} + 18 0^{\circ} n

3 x - 6^{\circ} = 6 0^{\circ} + 18 0^{\circ} n

Solve

3 x - 6^{\circ} = 6 0^{\circ} + 18 0^{\circ} n : x = \frac{18 0 ^{\circ} n}{3} + 2 2^{\circ}

3 x - 6^{\circ} = 6 0^{\circ} + 18 0^{\circ} n

Move

6^{\circ}

to the right side

3 x - 6^{\circ} = 6 0^{\circ} + 18 0^{\circ} n

Add

6^{\circ}

to both sides

3 x - 6^{\circ} + 6^{\circ} = 6 0^{\circ} + 18 0^{\circ} n + 6^{\circ}

Simplify

3 x - 6^{\circ} + 6^{\circ} = 6 0^{\circ} + 18 0^{\circ} n + 6^{\circ}

Simplify

3 x - 6^{\circ} + 6^{\circ} : 3 x

3 x - 6^{\circ} + 6^{\circ}

Add similar elements:

- 6^{\circ} + 6^{\circ} = 0

= 3 x

Simplify

6 0^{\circ} + 18 0^{\circ} n + 6^{\circ} : 18 0^{\circ} n + 6 6^{\circ}

6 0^{\circ} + 18 0^{\circ} n + 6^{\circ}

Group like terms

= 18 0^{\circ} n + 6 0^{\circ} + 6^{\circ}

Least Common Multiplier of

3, 30 : 30

3, 30

Least Common Multiplier (LCM)

Prime factorization of

3 : 3

3

3

is a prime number, therefore no factorization is possible

= 3

Prime factorization of

30 : 2 \cdot 3 \cdot 5

30

30

divides by

230 = 15 \cdot 2

= 2 \cdot 15

15

divides by

315 = 5 \cdot 3

= 2 \cdot 3 \cdot 5

2, 3, 5

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 3 \cdot 5

Multiply each factor the greatest number of times it occurs in either

3

30

= 3 \cdot 2 \cdot 5

Multiply the numbers:

3 \cdot 2 \cdot 5 = 30

= 30

Adjust Fractions based on the LCM

Multiply each numerator by the same amount needed to multiply its

corresponding denominator to turn it into the LCM

30

For

6 0^{\circ} :

multiply the denominator and numerator by

10

6 0^{\circ} = \frac{18 0 ^{\circ} 10}{3 \cdot 10} = 6 0^{\circ}

= 6 0^{\circ} + 6^{\circ}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{18 0 ^{\circ} 10 + 18 0 ^{\circ}}{30}

Add similar elements:

180 0^{\circ} + 18 0^{\circ} = 198 0^{\circ}

= 18 0^{\circ} n + 6 6^{\circ}

3 x = 18 0^{\circ} n + 6 6^{\circ}

3 x = 18 0^{\circ} n + 6 6^{\circ}

3 x = 18 0^{\circ} n + 6 6^{\circ}

Divide both sides by

3

3 x = 18 0^{\circ} n + 6 6^{\circ}

Divide both sides by

3

\frac{3 x}{3} = \frac{18 0 ^{\circ} n}{3} + \frac{6 6 ^{\circ}}{3}

Simplify

\frac{3 x}{3} = \frac{18 0 ^{\circ} n}{3} + \frac{6 6 ^{\circ}}{3}

Simplify

\frac{3 x}{3} : x

\frac{3 x}{3}

Divide the numbers:

\frac{3}{3} = 1

= x

Simplify

\frac{18 0 ^{\circ} n}{3} + \frac{6 6 ^{\circ}}{3} : \frac{18 0 ^{\circ} n}{3} + 2 2^{\circ}

\frac{18 0 ^{\circ} n}{3} + \frac{6 6 ^{\circ}}{3}

\frac{6 6 ^{\circ}}{3} = 2 2^{\circ}

\frac{6 6 ^{\circ}}{3}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{198 0 ^{\circ}}{30 \cdot 3}

Multiply the numbers:

30 \cdot 3 = 90

= 2 2^{\circ}

= \frac{18 0 ^{\circ} n}{3} + 2 2^{\circ}

x = \frac{18 0 ^{\circ} n}{3} + 2 2^{\circ}

x = \frac{18 0 ^{\circ} n}{3} + 2 2^{\circ}

x = \frac{18 0 ^{\circ} n}{3} + 2 2^{\circ}

x = \frac{18 0 ^{\circ} n}{3} + 2 2^{\circ}

Popular Examples

sec(x)=sqrt(4)

sec (x) = 4

(182.5)/(sin(36.6))=(248.6)/(sin(x))

\frac{182.5}{sin ( 36. 6 ^{\circ} )} = \frac{248.6}{sin ( x )}

sqrt(1-cos(3x))=2pi

1 - cos (3 x) = 2 π

(sin(x-4))(sin(x-1))=0

(sin (x - 4)) (sin (x - 1)) = 0

solvefor θ,r=(10)/(3+2cos(θ))solve for

θ, r = \frac{10}{3 + 2 cos ( θ )}

Frequently Asked Questions (FAQ)

What is the general solution for cot(3x-6)=(sqrt(3))/3 ?
The general solution for cot(3x-6)=(sqrt(3))/3 is x=(180n)/3+22