Solve for x in Radians sin(x)^2=1/4

Solve for x in Radians sin(x)^2=1/4
Take the square root of both sides of the equation to eliminate the exponent on the left side.
Simplify .
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Rewrite as .
Any root of is .
Simplify the denominator.
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Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
The complete solution is the result of both the positive and negative portions of the solution.
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First, use the positive value of the to find the first solution.
Next, use the negative value of the to find the second solution.
The complete solution is the result of both the positive and negative portions of the solution.
Set up each of the solutions to solve for .
Solve for in .
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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.
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 .
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 radians in both directions.
, for any integer
, for any integer
Solve for in .
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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 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.
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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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
, for any integer
List all of the solutions.
, for any integer
Consolidate the solutions.
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Consolidate and to .
, for any integer
Consolidate and to .
, for any integer
, for any integer
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Name

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

Interesting facts

  • 1365899768 has 64 divisors, whose sum is 4774677840
  • The reverse of 1365899768 is 8679985631
  • Previous prime number is 6217

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 62
  • Digital Root 8

Name

Name one billion five hundred sixty-two million seven hundred twenty-eight thousand eight hundred eighty-four

Interesting facts

  • 1562728884 has 16 divisors, whose sum is 4688186688
  • The reverse of 1562728884 is 4888272651
  • Previous prime number is 3

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 51
  • Digital Root 6

Name

Name two hundred seventy-one million seven hundred seventy-two thousand four hundred seventy-nine

Interesting facts

  • 271772479 has 4 divisors, whose sum is 296479080
  • The reverse of 271772479 is 974277172
  • Previous prime number is 11

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 46
  • Digital Root 1