Solve for x in Radians 2sin(x)^2-3sin(x)=-1

Solve for x in Radians 2sin(x)^2-3sin(x)=-1
Add to both sides of the equation.
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, .
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 .
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.
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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Move to the left of .
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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Add to both sides of the equation.
Take the inverse sine of both sides of the equation to extract from inside the sine.
Simplify the right side.
Tap for more steps...
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.
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...
Move to the left of .
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
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Name

Name one billion eighty-two million six hundred eighty-six thousand seven hundred eighty-four

Interesting facts

  • 1082686784 has 512 divisors, whose sum is 12563527680
  • The reverse of 1082686784 is 4876862801
  • Previous prime number is 1087

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 50
  • Digital Root 5

Name

Name ninety-seven million one hundred ninety-five thousand two hundred twelve

Interesting facts

  • 97195212 has 16 divisors, whose sum is 242988120
  • The reverse of 97195212 is 21259179
  • Previous prime number is 9

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 8
  • Sum of Digits 36
  • Digital Root 9

Name

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

Interesting facts

  • 1542971642 has 4 divisors, whose sum is 2314457466
  • The reverse of 1542971642 is 2461792451
  • Previous prime number is 2

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 41
  • Digital Root 5