# 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.
Divide each term in by .
Simplify the left side.
Cancel the common factor of .
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 .
Rewrite as .
Simplify the numerator.
Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
Simplify the denominator.
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.
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 .
Take the inverse secant of both sides of the equation to extract from inside the secant.
Simplify the right side.
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 .
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 .
Take the inverse secant of both sides of the equation to extract from inside the secant.
Simplify the right side.
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 .
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.
Consolidate and to .
, for any integer
Consolidate and to .
, for any integer
, for any integer
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### Name

Name one billion five hundred sixty-five million one hundred eighty-seven thousand nine hundred forty-three

### Interesting facts

• 1565187943 has 4 divisors, whose sum is 1573558120
• The reverse of 1565187943 is 3497815651
• Previous prime number is 187

### Basic properties

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

### Name

Name one billion four hundred thirty-three million three hundred six thousand six hundred sixty-six

### Interesting facts

• 1433306666 has 32 divisors, whose sum is 2454323328
• The reverse of 1433306666 is 6666033341
• Previous prime number is 53

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 38
• Digital Root 2

### Name

Name one billion five hundred forty-two million two hundred sixty-one thousand two hundred twelve

### Interesting facts

• 1542261212 has 16 divisors, whose sum is 3471027552
• The reverse of 1542261212 is 2121622451
• Previous prime number is 3833

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 26
• Digital Root 8