Solve for θ in Degrees 3sin(theta)^2-4=-4sin(theta)

Solve for θ in Degrees 3sin(theta)^2-4=-4sin(theta)
Add to both sides of the equation.
Factor by grouping.
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Reorder terms.
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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Evaluate .
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
, for any integer
Set equal to and solve for .
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Set equal to .
Solve for .
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Subtract from both sides of the equation.
The range of sine is . Since does not fall in this range, there is no solution.
No solution
No solution
No solution
The final solution is all the values that make true.
, for any integer
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Name

Name one billion eight hundred forty-three million three hundred sixty-three thousand eight hundred thirty-eight

Interesting facts

  • 1843363838 has 8 divisors, whose sum is 2780493480
  • The reverse of 1843363838 is 8383633481
  • Previous prime number is 179

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 47
  • Digital Root 2

Name

Name two billion twenty-four million one hundred fifty-eight thousand eight hundred sixty-eight

Interesting facts

  • 2024158868 has 8 divisors, whose sum is 4554357462
  • The reverse of 2024158868 is 8688514202
  • Previous prime number is 2

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 44
  • Digital Root 8

Name

Name one billion three hundred fifty-six million three hundred thirty-three thousand three hundred six

Interesting facts

  • 1356333306 has 32 divisors, whose sum is 2845756800
  • The reverse of 1356333306 is 6033336531
  • Previous prime number is 29

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 33
  • Digital Root 6