Solve for x 2sin(x)-sin(2x)=0

Solve for x 2sin(x)-sin(2x)=0
Factor out of .
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Factor out of .
Factor out of .
Factor out of .
Rewrite as .
Divide each term in by .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Divide by .
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Set the first factor equal to and solve.
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Set the first factor equal to .
Take the inverse sine of both sides of the equation to extract from inside the sine.
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.
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The period of the function can be calculated using .
Replace with in the formula for period.
Solve the equation.
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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
Set the next factor equal to and solve.
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Set the next factor equal to .
Subtract from both sides of the equation.
Multiply each term in by
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Multiply each term in by .
Multiply .
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Multiply by .
Multiply by .
Multiply by .
Take the inverse cosine of both sides of the equation to extract from inside the cosine.
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.
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The period of the function can be calculated using .
Replace with in the formula for period.
Solve the equation.
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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
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 sixteen million nine hundred ninety-four thousand four hundred ninety-two

Interesting facts

  • 16994492 has 32 divisors, whose sum is 40649040
  • The reverse of 16994492 is 29449961
  • Previous prime number is 491

Basic properties

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

Name

Name one hundred forty-five million six hundred seven thousand nine hundred ninety-seven

Interesting facts

  • 145607997 has 8 divisors, whose sum is 194446656
  • The reverse of 145607997 is 799706541
  • Previous prime number is 647

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 48
  • Digital Root 3

Name

Name two billion forty-four million six hundred forty-seven thousand nine hundred fifty-nine

Interesting facts

  • 2044647959 has 4 divisors, whose sum is 2078166840
  • The reverse of 2044647959 is 9597464402
  • Previous prime number is 61

Basic properties

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