Solve for θ in Degrees cot(theta)^2-6cot(theta)+8=0

Solve for θ in Degrees cot(theta)^2-6cot(theta)+8=0
Factor the left side of the equation.
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Let . Substitute for all occurrences of .
Factor using the AC method.
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Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .
Write the factored form using these integers.
Replace all occurrences of with .
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Set equal to and solve for .
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Set equal to .
Solve for .
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Add to both sides of the equation.
Take the inverse cotangent of both sides of the equation to extract from inside the cotangent.
Simplify the right side.
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Evaluate .
The cotangent function is positive in the first and third quadrants. To find the second solution, subtract the reference angle from to find the solution in the fourth quadrant.
Add and .
Find the period of .
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The period of the function can be calculated using .
Replace with in the formula for period.
The absolute value is the distance between a number and zero. The distance between and is .
Divide by .
The period of the function is so values will repeat every degrees in both directions.
, for any integer
, for any integer
, for any integer
Set equal to and solve for .
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Set equal to .
Solve for .
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Add to both sides of the equation.
Take the inverse cotangent of both sides of the equation to extract from inside the cotangent.
Simplify the right side.
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Evaluate .
The cotangent function is positive in the first and third quadrants. To find the second solution, subtract the reference angle from to find the solution in the fourth quadrant.
Add and .
Find the period of .
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The period of the function can be calculated using .
Replace with in the formula for period.
The absolute value is the distance between a number and zero. The distance between and is .
Divide by .
The period of the function is so values will repeat every degrees in both directions.
, for any integer
, for any integer
, for any integer
The final solution is all the values that make true.
, for any integer
Consolidate the answers.
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Consolidate and to .
, for any integer
Consolidate and to .
, for any integer
, for any integer
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Name

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

Interesting facts

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

Basic properties

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

Name

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

Interesting facts

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

Basic properties

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

Name

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

Interesting facts

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

Basic properties

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