Solve for x in Radians 2sin(x)^2+3cos(x)-3=0

Solve for x in Radians 2sin(x)^2+3cos(x)-3=0
Replace the with based on the identity.
Simplify each term.
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Apply the distributive property.
Multiply by .
Multiply by .
Subtract from .
Substitute for .
Factor the left side of the equation.
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Factor out of .
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Factor out of .
Factor out of .
Rewrite as .
Factor out of .
Factor out of .
Factor.
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Factor by grouping.
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For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .
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Factor out of .
Rewrite as plus
Apply the distributive property.
Factor out the greatest common factor from each group.
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Group the first two terms and the last two terms.
Factor out the greatest common factor (GCF) from each group.
Factor the polynomial by factoring out the greatest common factor, .
Remove unnecessary parentheses.
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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Add to 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 .
Set equal to and solve for .
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Set equal to .
Add to both sides of the equation.
The final solution is all the values that make true.
Substitute for .
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.
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
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.
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 radians in both directions.
, for any integer
, for any integer
List all of the solutions.
, for any integer
Consolidate and to .
, for any integer
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Name

Name one billion eight hundred thirty-seven million four hundred thirty-six thousand two hundred twenty-one

Interesting facts

  • 1837436221 has 8 divisors, whose sum is 1845392120
  • The reverse of 1837436221 is 1226347381
  • Previous prime number is 337

Basic properties

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

Name

Name two hundred fifty-one million seven hundred forty-five thousand seven hundred ninety-nine

Interesting facts

  • 251745799 has 4 divisors, whose sum is 251778600
  • The reverse of 251745799 is 997547152
  • Previous prime number is 20549

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 49
  • Digital Root 4

Name

Name one billion three hundred fourteen million two hundred eighty-seven thousand nine hundred forty-seven

Interesting facts

  • 1314287947 has 8 divisors, whose sum is 1342804400
  • The reverse of 1314287947 is 7497824131
  • Previous prime number is 811

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 46
  • Digital Root 1