Solve for ? sin(x)=-( square root of 2)/2

Solve for ? sin(x)=-( square root of 2)/2
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
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Name

Name one billion seven hundred eight million five hundred sixty-one thousand nine hundred sixteen

Interesting facts

  • 1708561916 has 8 divisors, whose sum is 3844264320
  • The reverse of 1708561916 is 6191658071
  • Previous prime number is 2

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 44
  • Digital Root 8

Name

Name four hundred eighty-eight million four hundred seventeen thousand six hundred twenty-seven

Interesting facts

  • 488417627 has 4 divisors, whose sum is 509653200
  • The reverse of 488417627 is 726714884
  • Previous prime number is 23

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 47
  • Digital Root 2

Name

Name three hundred ninety-five million four hundred forty thousand four hundred sixty-one

Interesting facts

  • 395440461 has 8 divisors, whose sum is 398665600
  • The reverse of 395440461 is 164044593
  • Previous prime number is 151

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 36
  • Digital Root 9