Solve for θ in Degrees -2cos(theta)^2+sin(theta)+1=0

Solve for θ in Degrees -2cos(theta)^2+sin(theta)+1=0
Replace the with based on the identity.
Simplify each term.
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Apply the distributive property.
Multiply by .
Multiply by .
Add and .
Substitute for .
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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Multiply by .
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, .
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 .
Subtract from 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 sine of both sides of the equation to extract from inside the sine.
Simplify the right side.
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The exact value of is .
The sine function is positive in the first and second quadrants. To find the second solution, subtract the reference angle from to find the solution in the second 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 sine of both sides of the equation to extract from inside the sine.
Simplify the right side.
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The exact value of is .
The sine function is negative in the third and fourth quadrants. To find the second solution, subtract the solution from , to find a reference angle. Next, add this reference angle to to find the solution in the third quadrant.
Simplify the expression to find the second solution.
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Subtract from .
The resulting angle of is positive, less than , and coterminal with .
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 .
Add to every negative angle to get positive angles.
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Add to to find the positive angle.
Subtract from .
List the new angles.
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 answers.
, for any integer
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Name

Name one billion six hundred six million four hundred seventeen thousand seven hundred eighty-three

Interesting facts

  • 1606417783 has 4 divisors, whose sum is 1607277328
  • The reverse of 1606417783 is 3877146061
  • Previous prime number is 1873

Basic properties

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

Name

Name one billion nine hundred forty million nine hundred forty-six thousand three hundred seventy-two

Interesting facts

  • 1940946372 has 32 divisors, whose sum is 5137800840
  • The reverse of 1940946372 is 2736490491
  • Previous prime number is 17

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 45
  • Digital Root 9

Name

Name one billion two hundred ninety-four million seven hundred twenty-nine thousand seven hundred eighty-five

Interesting facts

  • 1294729785 has 8 divisors, whose sum is 1334659392
  • The reverse of 1294729785 is 5879274921
  • Previous prime number is 43

Basic properties

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