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.
Tap for more steps...
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 one billion seven hundred seventy-six million five hundred twelve thousand six hundred twelve

Interesting facts

  • 1776512612 has 16 divisors, whose sum is 4568175360
  • The reverse of 1776512612 is 2162156771
  • Previous prime number is 7

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 38
  • Digital Root 2

Name

Name two billion twelve million three hundred seventy-four thousand thirty-two

Interesting facts

  • 2012374032 has 128 divisors, whose sum is 14051931840
  • The reverse of 2012374032 is 2304732102
  • Previous prime number is 29

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 24
  • Digital Root 6

Name

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

Interesting facts

  • 1672515932 has 16 divisors, whose sum is 3926776752
  • The reverse of 1672515932 is 2395152761
  • Previous prime number is 23

Basic properties

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