Solve for θ in Degrees sec(theta)^2-25=0

Solve for θ in Degrees sec(theta)^2-25=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.
Simplify .
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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 secant of both sides of the equation to extract from inside the secant.
Simplify the right side.
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Evaluate .
The secant function is positive in the first and fourth quadrants. To find the second solution, subtract the reference angle from to find the solution in the fourth 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
Solve for in .
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Take the inverse secant of both sides of the equation to extract from inside the secant.
Simplify the right side.
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Evaluate .
The secant function is negative in the second and third quadrants. To find the second solution, subtract the reference angle from to find the solution in the third 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
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 four hundred forty-six million two hundred ninety-three thousand two hundred four

Interesting facts

  • 1446293204 has 32 divisors, whose sum is 3347568000
  • The reverse of 1446293204 is 4023926441
  • Previous prime number is 239

Basic properties

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

Name

Name one billion four hundred eighteen million seven hundred five thousand eight hundred seventy-six

Interesting facts

  • 1418705876 has 32 divisors, whose sum is 3669200640
  • The reverse of 1418705876 is 6785078141
  • Previous prime number is 173

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 47
  • Digital Root 2

Name

Name one billion two hundred eighty-nine million five hundred ninety thousand five hundred ninety-one

Interesting facts

  • 1289590591 has 8 divisors, whose sum is 1370645120
  • The reverse of 1289590591 is 1950959821
  • Previous prime number is 103

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 49
  • Digital Root 4