Solve for θ in Degrees 16sec(theta)^2-25=0

Solve for θ in Degrees 16sec(theta)^2-25=0
Add to both sides of the equation.
Divide each term in by and simplify.
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Divide each term in by .
Simplify the left side.
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Cancel the common factor of .
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Cancel the common factor.
Divide by .
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 .
Simplify the numerator.
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Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
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 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 four hundred eighty-six million five hundred forty-two thousand five hundred seventy-two

Interesting facts

  • 486542572 has 16 divisors, whose sum is 1121421672
  • The reverse of 486542572 is 275245684
  • Previous prime number is 41

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 43
  • Digital Root 7

Name

Name six hundred forty million five hundred forty-one thousand two hundred eighty-five

Interesting facts

  • 640541285 has 8 divisors, whose sum is 768965496
  • The reverse of 640541285 is 582145046
  • Previous prime number is 2557

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 35
  • Digital Root 8

Name

Name eight hundred thirty-five million five hundred seventy-one thousand five hundred fifty

Interesting facts

  • 835571550 has 128 divisors, whose sum is 2638863360
  • The reverse of 835571550 is 055175538
  • Previous prime number is 209

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 39
  • Digital Root 3