Solve for x in Degrees 2sin(x)cos(x)=cos(x)

Solve for x in Degrees 2sin(x)cos(x)=cos(x)
Subtract from both sides of the equation.
Factor out of .
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Factor out of .
Factor out of .
Factor out of .
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 cosine of both sides of the equation to extract from inside the cosine.
Simplify the right side.
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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 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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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.
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 degrees 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
Consolidate and to .
, for any integer
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Name

Name one billion five hundred six million six hundred forty-three thousand one hundred one

Interesting facts

  • 1506643101 has 16 divisors, whose sum is 1690236800
  • The reverse of 1506643101 is 1013466051
  • Previous prime number is 487

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 27
  • Digital Root 9

Name

Name eight hundred fourteen million six hundred sixty thousand four hundred eighty

Interesting facts

  • 814660480 has 1024 divisors, whose sum is 16817155200
  • The reverse of 814660480 is 084066418
  • Previous prime number is 149

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 37
  • Digital Root 1

Name

Name one hundred eighty-eight million eight hundred twenty-four thousand six hundred eight

Interesting facts

  • 188824608 has 256 divisors, whose sum is 1602099000
  • The reverse of 188824608 is 806428881
  • Previous prime number is 189

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 45
  • Digital Root 9