Solve for x in Degrees 2(1-cos(x)^2)=3/2

Solve for x in Degrees 2(1-cos(x)^2)=3/2
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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Multiply the numerator by the reciprocal of the denominator.
Multiply .
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Multiply and .
Multiply by .
Move all terms not containing to the right side of the equation.
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Subtract from both sides of the equation.
To write as a fraction with a common denominator, multiply by .
Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
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Multiply by .
Subtract from .
Move the negative in front of the fraction.
Divide each term in by and simplify.
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Divide each term in by .
Simplify the left side.
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Dividing two negative values results in a positive value.
Divide by .
Simplify the right side.
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Dividing two negative values results in a positive value.
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 one billion six hundred twenty-eight million five hundred fifty-four thousand two hundred nineteen

Interesting facts

  • 1628554219 has 8 divisors, whose sum is 1724746608
  • The reverse of 1628554219 is 9124558261
  • Previous prime number is 6011

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 43
  • Digital Root 7

Name

Name one billion four hundred thirty-five million one hundred eighty-four thousand eight

Interesting facts

  • 1435184008 has 64 divisors, whose sum is 5082955416
  • The reverse of 1435184008 is 8004815341
  • Previous prime number is 41

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 34
  • Digital Root 7

Name

Name three hundred fifty-six million four hundred five thousand nine hundred five

Interesting facts

  • 356405905 has 8 divisors, whose sum is 428981184
  • The reverse of 356405905 is 509504653
  • Previous prime number is 331

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 37
  • Digital Root 1