Solve for θ in Degrees 2sin(theta)^2+3sin(theta)=0

Solve for θ in Degrees 2sin(theta)^2+3sin(theta)=0
Factor the left side of the equation.
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Let . Substitute for all occurrences of .
Factor out of .
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Factor out of .
Factor out of .
Factor out of .
Replace all occurrences of with .
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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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
, 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.
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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Move the negative in front of the fraction.
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
Consolidate the answers.
, for any integer
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Name

Name one billion seven hundred thirty million three hundred ninety-eight thousand two hundred fifty-one

Interesting facts

  • 1730398251 has 8 divisors, whose sum is 2307423744
  • The reverse of 1730398251 is 1528930371
  • Previous prime number is 13367

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 39
  • Digital Root 3

Name

Name four hundred eight million five hundred seven thousand one hundred seven

Interesting facts

  • 408507107 has 4 divisors, whose sum is 414604296
  • The reverse of 408507107 is 701705804
  • Previous prime number is 67

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 32
  • Digital Root 5

Name

Name four hundred sixty-six million seven hundred seventy-six thousand three hundred seven

Interesting facts

  • 466776307 has 4 divisors, whose sum is 467776296
  • The reverse of 466776307 is 703677664
  • Previous prime number is 467

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 46
  • Digital Root 1