# Solve for ? 2cos(x)+1=0

Solve for ? 2cos(x)+1=0
Subtract from both sides of the equation.
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Move the negative in front of the fraction.
Take the inverse cosine of both sides of the equation to extract from inside the cosine.
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.
Simplify .
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply by .
Subtract from .
Find the period.
The period of the function can be calculated using .
Replace with in the formula for period.
Solve the equation.
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 radians in both directions.
, for any integer
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### Name

Name one billion four hundred twelve million two hundred forty-nine thousand one hundred six

### Interesting facts

• 1412249106 has 8 divisors, whose sum is 2824498224
• The reverse of 1412249106 is 6019422141
• Previous prime number is 3

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 30
• Digital Root 3

### Name

Name two billion fifty-one million eighty-five thousand four hundred seventy-nine

### Interesting facts

• 2051085479 has 4 divisors, whose sum is 2171737584
• The reverse of 2051085479 is 9745801502
• Previous prime number is 17

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 41
• Digital Root 5

### Name

Name one billion three hundred forty-two million two hundred eighty-eight thousand three hundred thirteen

### Interesting facts

• 1342288313 has 4 divisors, whose sum is 1385587968
• The reverse of 1342288313 is 3138822431
• Previous prime number is 31

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 35
• Digital Root 8