Solve for θ in Degrees csc(theta)^2-9csc(theta)+20=0

Solve for θ in Degrees csc(theta)^2-9csc(theta)+20=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 cosecant of both sides of the equation to extract from inside the cosecant.
Simplify the right side.
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Evaluate .
The cosecant function is positive in the first and second quadrants. To find the second solution, subtract the reference angle from to find the solution in the second quadrant.
Subtract from .
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 cosecant of both sides of the equation to extract from inside the cosecant.
Simplify the right side.
Tap for more steps...
Evaluate .
The cosecant function is positive in the first and second quadrants. To find the second solution, subtract the reference angle from to find the solution in the second quadrant.
Subtract from .
Find the period of .
Tap for more steps...
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
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Name

Name one billion six hundred sixty-two million three hundred twelve thousand eight hundred ninety-one

Interesting facts

  • 1662312891 has 16 divisors, whose sum is 2257355520
  • The reverse of 1662312891 is 1982132661
  • Previous prime number is 503

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 39
  • Digital Root 3

Name

Name four hundred seventy-seven million twenty-six thousand six hundred seventy-nine

Interesting facts

  • 477026679 has 4 divisors, whose sum is 636035576
  • The reverse of 477026679 is 976620774
  • Previous prime number is 3

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 48
  • Digital Root 3

Name

Name one hundred seventy-two million two hundred seventy-four thousand five hundred twenty-nine

Interesting facts

  • 172274529 has 8 divisors, whose sum is 186702120
  • The reverse of 172274529 is 925472271
  • Previous prime number is 29

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 39
  • Digital Root 3