Solve for θ in Degrees cos(theta)^2-cos(theta)=0

Solve for θ in Degrees cos(theta)^2-cos(theta)=0
Factor the left side of the equation.
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Let . Substitute for all occurrences of .
Factor out of .
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Factor out of .
Factor out of .
Factor out of .
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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Take the inverse cosine of both sides of the equation to extract from inside the cosine.
Simplify the right side.
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The exact value of is .
The cosine function is positive in the first and fourth quadrants. To find the second solution, subtract the reference angle from to find the solution in the fourth 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 cosine of both sides of the equation to extract from inside the cosine.
Simplify the right side.
Tap for more steps...
The exact value of is .
The cosine function is positive in the first and fourth quadrants. To find the second solution, subtract the reference angle from to find the solution in the fourth 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
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 six hundred eleven million nine hundred seventy-one thousand nine hundred sixty-four

Interesting facts

  • 611971964 has 16 divisors, whose sum is 1377235656
  • The reverse of 611971964 is 469179116
  • Previous prime number is 27661

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 44
  • Digital Root 8

Name

Name nine hundred seventy-seven million six hundred twenty-nine thousand two hundred eighty-seven

Interesting facts

  • 977629287 has 16 divisors, whose sum is 1373567360
  • The reverse of 977629287 is 782926779
  • Previous prime number is 17203

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 57
  • Digital Root 3

Name

Name one billion nine hundred twenty-eight million three hundred seventy thousand three hundred twelve

Interesting facts

  • 1928370312 has 128 divisors, whose sum is 7199860608
  • The reverse of 1928370312 is 2130738291
  • Previous prime number is 113

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 36
  • Digital Root 9