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 eight hundred fifteen million three hundred fifty-four thousand five hundred sixty-one

Interesting facts

  • 1815354561 has 16 divisors, whose sum is 2449832000
  • The reverse of 1815354561 is 1654535181
  • Previous prime number is 349

Basic properties

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

Name

Name one billion three hundred fifty-one million six hundred forty-six thousand six hundred sixty-two

Interesting facts

  • 1351646662 has 32 divisors, whose sum is 2174860800
  • The reverse of 1351646662 is 2666461531
  • Previous prime number is 61

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 40
  • Digital Root 4

Name

Name two hundred seventy-seven million three hundred sixty-two thousand three hundred sixty-three

Interesting facts

  • 277362363 has 16 divisors, whose sum is 388224000
  • The reverse of 277362363 is 363263772
  • Previous prime number is 59

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 39
  • Digital Root 3