Let <math><mstyle displaystyle="true"><mi>u</mi><mo>=</mo><mi>cot</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> . Substitute <math><mstyle displaystyle="true"><mi>u</mi></mstyle></math> for all occurrences of <math><mstyle displaystyle="true"><mi>cot</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> .

Factor <math><mstyle displaystyle="true"><msup><mrow><mi>u</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>-</mo><mn>6</mn><mi>u</mi><mo>+</mo><mn>8</mn></mstyle></math> using the AC method.

Consider the form <math><mstyle displaystyle="true"><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mi>b</mi><mi>x</mi><mo>+</mo><mi>c</mi></mstyle></math> . Find a pair of integers whose product is <math><mstyle displaystyle="true"><mi>c</mi></mstyle></math> and whose sum is <math><mstyle displaystyle="true"><mi>b</mi></mstyle></math> . In this case, whose product is <math><mstyle displaystyle="true"><mn>8</mn></mstyle></math> and whose sum is <math><mstyle displaystyle="true"><mo>-</mo><mn>6</mn></mstyle></math> .

Write the factored form using these integers.

Replace all occurrences of <math><mstyle displaystyle="true"><mi>u</mi></mstyle></math> with <math><mstyle displaystyle="true"><mi>cot</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> .

If any individual factor on the left side of the equation is equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> , the entire expression will be equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Set <math><mstyle displaystyle="true"><mi>cot</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mo>-</mo><mn>4</mn></mstyle></math> equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Solve <math><mstyle displaystyle="true"><mi>cot</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mo>-</mo><mn>4</mn><mo>=</mo><mn>0</mn></mstyle></math> for <math><mstyle displaystyle="true"><mi>θ</mi></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> to both sides of the equation.

Take the inverse cotangent of both sides of the equation to extract <math><mstyle displaystyle="true"><mi>θ</mi></mstyle></math> from inside the cotangent.

Simplify the right side.

Evaluate <math><mstyle displaystyle="true"><mi>arccot</mi><mrow><mo>(</mo><mn>4</mn><mo>)</mo></mrow></mstyle></math> .

The cotangent function is positive in the first and third quadrants. To find the second solution, subtract the reference angle from <math><mstyle displaystyle="true"><mn>180</mn></mstyle></math> to find the solution in the fourth quadrant.

Add <math><mstyle displaystyle="true"><mn>180</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>14.03624346</mn></mstyle></math> .

Find the period of <math><mstyle displaystyle="true"><mi>cot</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> .

The period of the function can be calculated using <math><mstyle displaystyle="true"><mfrac><mrow><mn>180</mn></mrow><mrow><mrow><mo>|</mo><mi>b</mi><mo>|</mo></mrow></mrow></mfrac></mstyle></math> .

Replace <math><mstyle displaystyle="true"><mi>b</mi></mstyle></math> with <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> in the formula for period.

The absolute value is the distance between a number and zero. The distance between <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> is <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Divide <math><mstyle displaystyle="true"><mn>180</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

The period of the <math><mstyle displaystyle="true"><mi>cot</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> function is <math><mstyle displaystyle="true"><mn>180</mn></mstyle></math> so values will repeat every <math><mstyle displaystyle="true"><mn>180</mn></mstyle></math> degrees in both directions.

Set <math><mstyle displaystyle="true"><mi>cot</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mo>-</mo><mn>2</mn></mstyle></math> equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Solve <math><mstyle displaystyle="true"><mi>cot</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mo>-</mo><mn>2</mn><mo>=</mo><mn>0</mn></mstyle></math> for <math><mstyle displaystyle="true"><mi>θ</mi></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> to both sides of the equation.

Take the inverse cotangent of both sides of the equation to extract <math><mstyle displaystyle="true"><mi>θ</mi></mstyle></math> from inside the cotangent.

Simplify the right side.

Evaluate <math><mstyle displaystyle="true"><mi>arccot</mi><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow></mstyle></math> .

The cotangent function is positive in the first and third quadrants. To find the second solution, subtract the reference angle from <math><mstyle displaystyle="true"><mn>180</mn></mstyle></math> to find the solution in the fourth quadrant.

Add <math><mstyle displaystyle="true"><mn>180</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>26.56505117</mn></mstyle></math> .

Find the period of <math><mstyle displaystyle="true"><mi>cot</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> .

The period of the function can be calculated using <math><mstyle displaystyle="true"><mfrac><mrow><mn>180</mn></mrow><mrow><mrow><mo>|</mo><mi>b</mi><mo>|</mo></mrow></mrow></mfrac></mstyle></math> .

Replace <math><mstyle displaystyle="true"><mi>b</mi></mstyle></math> with <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> in the formula for period.

The absolute value is the distance between a number and zero. The distance between <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> is <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Divide <math><mstyle displaystyle="true"><mn>180</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

The period of the <math><mstyle displaystyle="true"><mi>cot</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> function is <math><mstyle displaystyle="true"><mn>180</mn></mstyle></math> so values will repeat every <math><mstyle displaystyle="true"><mn>180</mn></mstyle></math> degrees in both directions.

The final solution is all the values that make <math><mstyle displaystyle="true"><mrow><mo>(</mo><mi>cot</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mo>-</mo><mn>4</mn><mo>)</mo></mrow><mrow><mo>(</mo><mi>cot</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mo>-</mo><mn>2</mn><mo>)</mo></mrow><mo>=</mo><mn>0</mn></mstyle></math> true.

Consolidate <math><mstyle displaystyle="true"><mn>14.03624346</mn><mo>+</mo><mn>180</mn><mi>n</mi></mstyle></math> and <math><mstyle displaystyle="true"><mn>194.03624346</mn><mo>+</mo><mn>180</mn><mi>n</mi></mstyle></math> to <math><mstyle displaystyle="true"><mn>14.03624346</mn><mo>+</mo><mn>180</mn><mi>n</mi></mstyle></math> .

Consolidate <math><mstyle displaystyle="true"><mn>26.56505117</mn><mo>+</mo><mn>180</mn><mi>n</mi></mstyle></math> and <math><mstyle displaystyle="true"><mn>206.56505117</mn><mo>+</mo><mn>180</mn><mi>n</mi></mstyle></math> to <math><mstyle displaystyle="true"><mn>26.56505117</mn><mo>+</mo><mn>180</mn><mi>n</mi></mstyle></math> .

Do you know how to Solve for θ in Degrees cot(theta)^2-6cot(theta)+8=0? If not, you can write to our math experts in our application. The best solution for your task you can find above on this page.

Name | one billion three hundred twenty-one million five hundred thirteen thousand six hundred twenty-one |
---|

- 1321513621 has 4 divisors, whose sum is
**1321632000** - The reverse of 1321513621 is
**1263151231** - Previous prime number is
**12479**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 25
- Digital Root 7

Name | nine hundred sixty-four million two hundred fifty-six thousand three hundred fifty-one |
---|

- 964256351 has 8 divisors, whose sum is
**997864320** - The reverse of 964256351 is
**153652469** - Previous prime number is
**7477**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 41
- Digital Root 5

Name | one billion six hundred seven million five hundred thirty-two thousand six hundred seventy-three |
---|

- 1607532673 has 8 divisors, whose sum is
**1655750592** - The reverse of 1607532673 is
**3762357061** - Previous prime number is
**347**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 40
- Digital Root 4