Solve for x sin(2x)=-1

Solve for x sin(2x)=-1
Take the inverse sine of both sides of the equation to extract from inside the sine.
The exact value of is .
Divide each term by and simplify.
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Divide each term in by .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Multiply .
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Multiply and .
Multiply by .
The sine function is negative in the third and fourth quadrants. To find the second solution, subtract the solution from , to find a reference angle. Next, add this reference angle to to find the solution in the third quadrant.
Simplify the expression to find the second solution.
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To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Combine.
Multiply by .
Combine the numerators over the common denominator.
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Combine.
Multiply by .
Combine the numerators over the common denominator.
Add and .
Multiply by .
Add and .
Divide each term by and simplify.
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Divide each term in by .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Multiply .
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Multiply and .
Multiply by .
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 .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Add to every negative angle to get positive angles.
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Add to to find the positive angle.
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
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Move to the left of .
Subtract from .
List the new angles.
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 two hundred sixty million fifty-three thousand eight hundred ninety-one

Interesting facts

  • 260053891 has 8 divisors, whose sum is 263343600
  • The reverse of 260053891 is 198350062
  • Previous prime number is 389

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 34
  • Digital Root 7

Name

Name one billion one hundred forty-three million nine hundred thirty-one thousand eight hundred seventy-two

Interesting facts

  • 1143931872 has 256 divisors, whose sum is 11828788992
  • The reverse of 1143931872 is 2781393411
  • Previous prime number is 47

Basic properties

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

Name

Name six hundred thirty-eight million four hundred twenty-two thousand five

Interesting facts

  • 638422005 has 32 divisors, whose sum is 1184674176
  • The reverse of 638422005 is 500224836
  • Previous prime number is 13

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 30
  • Digital Root 3