Solve for x cos(2x)=-1/2

Solve for x cos(2x)=-1/2
Take the inverse cosine of both sides of the equation to extract from inside the cosine.
The exact value of is .
Divide each term by and simplify.
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Divide each term in by .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Cancel the common factor of .
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Factor out of .
Cancel the common factor.
Rewrite the expression.
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 the expression to find the second solution.
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To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Combine.
Multiply by .
Combine the numerators over the common denominator.
Multiply by .
Subtract from .
Divide each term by and simplify.
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Divide each term in by .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Cancel the common factor of .
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Find the period.
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The period of the function can be calculated using .
Replace with in the formula for period.
Solve the equation.
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The absolute value is the distance between a number and zero. The distance between and is .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
The period of the function is so values will repeat every radians in both directions.
, for any integer
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Name

Name four hundred ninety-four million three hundred seventy-three thousand six hundred eight

Interesting facts

  • 494373608 has 32 divisors, whose sum is 1673471124
  • The reverse of 494373608 is 806373494
  • Previous prime number is 337

Basic properties

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

Name

Name one billion six hundred thirty-three million seven hundred fifty thousand five hundred thirty-four

Interesting facts

  • 1633750534 has 32 divisors, whose sum is 2709715680
  • The reverse of 1633750534 is 4350573361
  • Previous prime number is 509

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 37
  • Digital Root 1

Name

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

Interesting facts

  • 679721726 has 8 divisors, whose sum is 1043293944
  • The reverse of 679721726 is 627127976
  • Previous prime number is 43

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 47
  • Digital Root 2