Solve for x in Radians cos(x)-sin(x)=0

Solve for x in Radians cos(x)-sin(x)=0
Divide each term in the equation by .
Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Separate fractions.
Convert from to .
Divide by .
Separate fractions.
Convert from to .
Divide by .
Multiply by .
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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Dividing two negative values results in a positive value.
Divide by .
Simplify the right side.
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Divide by .
Take the inverse tangent of both sides of the equation to extract from inside the tangent.
Simplify the right side.
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The exact value of is .
The tangent function is positive in the first and third quadrants. To find the second solution, add the reference angle from to find the solution in the fourth quadrant.
Simplify .
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To write as a fraction with a common denominator, multiply by .
Combine fractions.
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Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
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Move to the left of .
Add and .
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 radians in both directions.
, for any integer
Consolidate the answers.
, for any integer
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Name

Name six hundred eighty-two million one hundred fifty-nine thousand nine hundred eighty-seven

Interesting facts

  • 682159987 has 4 divisors, whose sum is 682525296
  • The reverse of 682159987 is 789951286
  • Previous prime number is 1877

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 55
  • Digital Root 1

Name

Name two billion one hundred eight million eight hundred forty-two thousand five hundred sixty-five

Interesting facts

  • 2108842565 has 16 divisors, whose sum is 2625822192
  • The reverse of 2108842565 is 5652488012
  • Previous prime number is 97

Basic properties

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

Name

Name seven hundred fifty-one million seven hundred eighty-two thousand seven hundred sixty-one

Interesting facts

  • 751782761 has 8 divisors, whose sum is 805671744
  • The reverse of 751782761 is 167287157
  • Previous prime number is 23

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 44
  • Digital Root 8