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 one billion seven hundred thirty-eight million five hundred ninety-four thousand seven hundred forty-one

Interesting facts

  • 1738594741 has 8 divisors, whose sum is 1874409824
  • The reverse of 1738594741 is 1474958371
  • Previous prime number is 907

Basic properties

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

Name

Name two billion fifty-five million six hundred seventy-five thousand three hundred seventy-two

Interesting facts

  • 2055675372 has 64 divisors, whose sum is 6322402944
  • The reverse of 2055675372 is 2735765502
  • Previous prime number is 571

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 42
  • Digital Root 6

Name

Name one billion three hundred nine million two hundred fourteen thousand seven hundred sixty

Interesting facts

  • 1309214760 has 256 divisors, whose sum is 8505077760
  • The reverse of 1309214760 is 0674129031
  • Previous prime number is 7

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 33
  • Digital Root 6