Solve for x sin(x)=-1

Solve for x sin(x)=-1
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 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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Simplify .
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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.
Simplify the numerator.
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Multiply by .
Add and .
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 .
Add and .
Subtract from .
The resulting angle of is positive, less than , and coterminal with .
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 .
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 .
Tap for more steps...
Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
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Multiply by .
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 one billion one hundred sixty-three million five hundred sixty-nine thousand eight hundred thirty

Interesting facts

  • 1163569830 has 32 divisors, whose sum is 2800203264
  • The reverse of 1163569830 is 0389653611
  • Previous prime number is 367

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 42
  • Digital Root 6

Name

Name two billion forty million five hundred thirty-six thousand seven hundred eighty

Interesting facts

  • 2040536780 has 16 divisors, whose sum is 5509449360
  • The reverse of 2040536780 is 0876350402
  • Previous prime number is 5

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 35
  • Digital Root 8

Name

Name one billion ninety-six million eight hundred thirty-eight thousand seven hundred ten

Interesting facts

  • 1096838710 has 16 divisors, whose sum is 1706787936
  • The reverse of 1096838710 is 0178386901
  • Previous prime number is 53

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 43
  • Digital Root 7