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

Solve for θ in Degrees cos(theta)^2=1/2
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 .
Multiply by .
Combine and simplify the denominator.
Multiply and .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Rewrite as .
Use to rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Evaluate the exponent.
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
, for any integer
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### Name

Name seven hundred fifty million eight hundred six thousand nine hundred

### Interesting facts

• 750806900 has 16 divisors, whose sum is 1756888380
• The reverse of 750806900 is 009608057
• Previous prime number is 25

### Basic properties

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

### Name

Name five million nine hundred forty-seven thousand nine hundred ninety-six

### Interesting facts

• 5947996 has 8 divisors, whose sum is 13383000
• The reverse of 5947996 is 6997495
• Previous prime number is 2

### Basic properties

• Is Prime? no
• Number parity even
• Number length 7
• Sum of Digits 49
• Digital Root 4

### Name

Name one billion four hundred five million two hundred fourteen thousand four hundred sixty-four

### Interesting facts

• 1405214464 has 2048 divisors, whose sum is 38093690880
• The reverse of 1405214464 is 4644125041
• Previous prime number is 251

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 31
• Digital Root 4