Solve for x in Degrees sin(x)^2+sin(x)=0

Solve for x in Degrees sin(x)^2+sin(x)=0
Factor the left side of the equation.
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Let . Substitute for all occurrences of .
Factor out of .
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Factor out of .
Raise to the power of .
Factor out of .
Factor out of .
Replace all occurrences of with .
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 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 .
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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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Subtract from both sides of the equation.
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 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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Subtract from .
The resulting angle of is positive, less than , and coterminal with .
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 .
Add to every negative angle to get positive angles.
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Add to to find the positive angle.
Subtract from .
List the new angles.
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 seven hundred seventy-six million four hundred seventy-four thousand one hundred ninety

Interesting facts

  • 776474190 has 32 divisors, whose sum is 1669545984
  • The reverse of 776474190 is 091474677
  • Previous prime number is 127

Basic properties

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

Name

Name four hundred twenty-four million seven hundred eighty-six thousand seven hundred two

Interesting facts

  • 424786702 has 8 divisors, whose sum is 639481176
  • The reverse of 424786702 is 207687424
  • Previous prime number is 277

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 40
  • Digital Root 4

Name

Name one billion two hundred ninety million nine hundred fifty-three thousand seven hundred ninety

Interesting facts

  • 1290953790 has 64 divisors, whose sum is 3151872000
  • The reverse of 1290953790 is 0973590921
  • Previous prime number is 1367

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 45
  • Digital Root 9