Solve for θ in Radians 2cos(theta)^2+cos(theta)=0

Solve for θ in Radians 2cos(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 .
Raise to the power 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.
Simplify .
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To write as a fraction with a common denominator, multiply by .
Combine fractions.
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Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
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Multiply by .
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 radians 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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Subtract from both sides of the equation.
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 .
Simplify the right side.
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Move the negative in front of the fraction.
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 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.
Simplify .
Tap for more steps...
To write as a fraction with a common denominator, multiply by .
Combine fractions.
Tap for more steps...
Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
Tap for more steps...
Multiply by .
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 radians 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 and to .
, for any integer
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Name

Name eight hundred seventy million seven hundred forty-six thousand seven hundred eleven

Interesting facts

  • 870746711 has 4 divisors, whose sum is 871306800
  • The reverse of 870746711 is 117647078
  • Previous prime number is 1559

Basic properties

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

Name

Name one billion one hundred twenty-two million four thousand six hundred five

Interesting facts

  • 1122004605 has 4 divisors, whose sum is 1196804928
  • The reverse of 1122004605 is 5064002211
  • Previous prime number is 15

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 21
  • Digital Root 3

Name

Name one hundred ninety-eight million six hundred eighty-seven thousand four hundred ninety-five

Interesting facts

  • 198687495 has 16 divisors, whose sum is 322646400
  • The reverse of 198687495 is 594786891
  • Previous prime number is 67

Basic properties

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