What is the general solution for -3sqrt(3)cot(θ)+5=14 ?

The general solution for -3sqrt(3)cot(θ)+5=14 is θ=(5pi)/6+pin

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Popular >

-3sqrt(3)cot(θ)+5=14

Solution

- 33 cot (θ) + 5 = 14

Solution

θ = \frac{5 π}{6} + πn

Degrees

θ = 15 0^{\circ} + 18 0^{\circ} n

Solution steps

- 33 cot (θ) + 5 = 14

Move

5

to the right side

- 33 cot (θ) + 5 = 14

Subtract

5

from both sides

- 33 cot (θ) + 5 - 5 = 14 - 5

Simplify

- 33 cot (θ) = 9

- 33 cot (θ) = 9

Divide both sides by

- 33

- 33 cot (θ) = 9

Divide both sides by

- 33

\frac{- 3 3 cot ( θ )}{- 3 3} = \frac{9}{- 3 3}

Simplify

\frac{- 3 3 cot ( θ )}{- 3 3} = \frac{9}{- 3 3}

Simplify

\frac{- 3 3 cot ( θ )}{- 3 3} : cot (θ)

\frac{- 3 3 cot ( θ )}{- 3 3}

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

= \frac{3 3 cot ( θ )}{3 3}

Divide the numbers:

\frac{3}{3} = 1

= \frac{3 cot ( θ )}{3}

Cancel the common factor:

3

= cot (θ)

Simplify

\frac{9}{- 3 3} : - 3

\frac{9}{- 3 3}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{9}{3 3}

Divide the numbers:

\frac{9}{3} = 3

= \frac{3}{3}

Apply radical rule:

3 = 3^{\frac{1}{2}}

= \frac{3}{3 ^{\frac{1}{2}}}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = x^{a - b}

\frac{3 ^{1}}{3 ^{\frac{1}{2}}} = 3^{1 - \frac{1}{2}}

= 3^{1 - \frac{1}{2}}

Subtract the numbers:

1 - \frac{1}{2} = \frac{1}{2}

= 3^{\frac{1}{2}}

Apply radical rule:

3^{\frac{1}{2}} = 3

= - 3

cot (θ) = - 3

cot (θ) = - 3

cot (θ) = - 3

General solutions for

cot (θ) = - 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

θ = \frac{5 π}{6} + πn

θ = \frac{5 π}{6} + πn

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Frequently Asked Questions (FAQ)

What is the general solution for -3sqrt(3)cot(θ)+5=14 ?
The general solution for -3sqrt(3)cot(θ)+5=14 is θ=(5pi)/6+pin