# Solve for ? cos(x)=-1/2

Solve for ? cos(x)=-1/2
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 six hundred seventy-seven million four hundred fifteen thousand two hundred fifty

### Interesting facts

• 1677415250 has 32 divisors, whose sum is 3588713856
• The reverse of 1677415250 is 0525147761
• Previous prime number is 5

### Basic properties

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

### Name

Name one billion two hundred fifty-three million one hundred forty-four thousand sixty-two

### Interesting facts

• 1253144062 has 8 divisors, whose sum is 1940352192
• The reverse of 1253144062 is 2604413521
• Previous prime number is 31

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 28
• Digital Root 1

### Name

Name one billion seven hundred twelve million nine hundred forty-four thousand one hundred forty

### Interesting facts

• 1712944140 has 32 divisors, whose sum is 3951673344
• The reverse of 1712944140 is 0414492171
• Previous prime number is 47

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 33
• Digital Root 6