# Solve for θ in Degrees 4cos(theta)^2=1

Solve for θ in Degrees 4cos(theta)^2=1
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 .
Any root of is .
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 cosine of both sides of the equation to extract from inside the cosine.
Simplify the right side.
The exact value of is .
The cosine 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 cosine of both sides of the equation to extract from inside the cosine.
Simplify the right side.
The exact value of is .
The cosine 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 eighty-nine million nine hundred twenty thousand two hundred sixty-three

### Interesting facts

• 89920263 has 4 divisors, whose sum is 119893688
• The reverse of 89920263 is 36202998
• Previous prime number is 3

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 8
• Sum of Digits 39
• Digital Root 3

### Name

Name one billion seven hundred twenty-eight million six hundred thirty-nine thousand six hundred eighty-nine

### Interesting facts

• 1728639689 has 8 divisors, whose sum is 1804941600
• The reverse of 1728639689 is 9869368271
• Previous prime number is 43

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 59
• Digital Root 5

### Name

Name one billion six hundred seventy-three million three hundred thirty-six thousand thirty-seven

### Interesting facts

• 1673336037 has 8 divisors, whose sum is 2231336800
• The reverse of 1673336037 is 7306333761
• Previous prime number is 13171

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 39
• Digital Root 3