# 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 .
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 eight hundred nineteen million six hundred three thousand three hundred sixty-four

### Interesting facts

• 819603364 has 8 divisors, whose sum is 1844107578
• The reverse of 819603364 is 463306918
• Previous prime number is 2

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 40
• Digital Root 4

### Name

Name one billion two hundred ninety-seven million eight hundred ninety-six thousand fifty-two

### Interesting facts

• 1297896052 has 8 divisors, whose sum is 2920266126
• The reverse of 1297896052 is 2506987921
• Previous prime number is 2

### Basic properties

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

### Name

Name one hundred eighty-nine million two hundred fifty-five thousand two hundred sixty

### Interesting facts

• 189255260 has 32 divisors, whose sum is 511585200
• The reverse of 189255260 is 062552981
• Previous prime number is 937

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 38
• Digital Root 2