Solve for θ in Degrees 4cos(theta)^2=1

Solve for θ in Degrees 4cos(theta)^2=1
Divide each term in by and simplify.
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Divide each term in by .
Simplify the left side.
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Cancel the common factor of .
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Cancel the common factor.
Divide by .
Take the square root of both sides of the equation to eliminate the exponent on the left side.
Simplify .
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Rewrite as .
Any root of is .
Simplify the denominator.
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Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
The complete solution is the result of both the positive and negative portions of the solution.
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First, use the positive value of the to find the first solution.
Next, use the negative value of the to find the second solution.
The complete solution is the result of both the positive and negative portions of the solution.
Set up each of the solutions to solve for .
Solve for in .
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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
Solve for in .
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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 negative in the second and third quadrants. To find the second solution, subtract the reference angle from to find the solution in the third 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
List all of the solutions.
, for any integer
Consolidate the solutions.
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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 eight hundred ninety-eight million six hundred thousand five hundred fifty-five

Interesting facts

  • 898600555 has 4 divisors, whose sum is 1078320672
  • The reverse of 898600555 is 555006898
  • Previous prime number is 5

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 46
  • Digital Root 1

Name

Name one billion one hundred eighty-eight million seven hundred sixty-nine thousand four hundred nineteen

Interesting facts

  • 1188769419 has 8 divisors, whose sum is 1761139920
  • The reverse of 1188769419 is 9149678811
  • Previous prime number is 9

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 54
  • Digital Root 9

Name

Name one billion two hundred ninety-seven million eight hundred sixteen thousand nine hundred ninety-three

Interesting facts

  • 1297816993 has 16 divisors, whose sum is 1454806080
  • The reverse of 1297816993 is 3996187921
  • Previous prime number is 337

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 55
  • Digital Root 1