What is the general solution for -5sqrt(3)cot(θ)+1=16 ?

The general solution for -5sqrt(3)cot(θ)+1=16 is θ=(5pi)/6+pin

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Popular >

-5sqrt(3)cot(θ)+1=16

Solution

- 53 cot (θ) + 1 = 16

Solution

θ = \frac{5 π}{6} + πn

Degrees

θ = 15 0^{\circ} + 18 0^{\circ} n

Solution steps

- 53 cot (θ) + 1 = 16

Move

1

to the right side

- 53 cot (θ) + 1 = 16

Subtract

1

from both sides

- 53 cot (θ) + 1 - 1 = 16 - 1

Simplify

- 53 cot (θ) = 15

- 53 cot (θ) = 15

Divide both sides by

- 53

- 53 cot (θ) = 15

Divide both sides by

- 53

\frac{- 5 3 cot ( θ )}{- 5 3} = \frac{15}{- 5 3}

Simplify

\frac{- 5 3 cot ( θ )}{- 5 3} = \frac{15}{- 5 3}

Simplify

\frac{- 5 3 cot ( θ )}{- 5 3} : cot (θ)

\frac{- 5 3 cot ( θ )}{- 5 3}

Apply the fraction rule:

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

= \frac{5 3 cot ( θ )}{5 3}

Divide the numbers:

\frac{5}{5} = 1

= \frac{3 cot ( θ )}{3}

Cancel the common factor:

3

= cot (θ)

Simplify

\frac{15}{- 5 3} : - 3

\frac{15}{- 5 3}

Apply the fraction rule:

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

= - \frac{15}{5 3}

Divide the numbers:

\frac{15}{5} = 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

Popular Examples

-sin(x)=sin(x)

- sin (x) = sin (x)

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

2 sin^{2} (x) + 4 sin (x) + 2 = 0

2sin(θ)=csc(θ)

2 sin (θ) = csc (θ)

cos(θ)=-0.7

cos (θ) = - 0.7

2cos^2(x)+7cos(x)+5=0

2 cos^{2} (x) + 7 cos (x) + 5 = 0

Frequently Asked Questions (FAQ)

What is the general solution for -5sqrt(3)cot(θ)+1=16 ?
The general solution for -5sqrt(3)cot(θ)+1=16 is θ=(5pi)/6+pin