Solve for θ in Radians sin(theta)^2-1=0

Solve for θ in Radians sin(theta)^2-1=0
Add to both sides of the equation.
Take the square root of both sides of the equation to eliminate the exponent on the left side.
Any root of is .
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 answers.
, for any integer
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Name

Name nine hundred seventy-seven million five hundred fifty-five thousand five hundred twenty-four

Interesting facts

  • 977555524 has 32 divisors, whose sum is 2401941600
  • The reverse of 977555524 is 425555779
  • Previous prime number is 22019

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 49
  • Digital Root 4

Name

Name eight hundred seventy-six million nine hundred sixty-two thousand seven hundred seventy-two

Interesting facts

  • 876962772 has 64 divisors, whose sum is 4008973824
  • The reverse of 876962772 is 277269678
  • Previous prime number is 3

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 54
  • Digital Root 9

Name

Name five hundred five million two hundred seventy-seven thousand one hundred ninety-six

Interesting facts

  • 505277196 has 128 divisors, whose sum is 1732104000
  • The reverse of 505277196 is 691772505
  • Previous prime number is 53

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 42
  • Digital Root 6