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

Solve for x cos(2x)=1/2
Take the inverse cosine of both sides of the equation to extract from inside the cosine.
The exact value of is .
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Multiply .
Multiply and .
Multiply by .
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.
Simplify the expression to find the second solution.
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.
Multiply by .
Subtract from .
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Multiply .
Multiply and .
Multiply by .
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 .
Cancel the common factor of .
Cancel the common factor.
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 three hundred seventy-seven million four hundred ninety-nine thousand three hundred fifty-five

### Interesting facts

• 377499355 has 8 divisors, whose sum is 458457552
• The reverse of 377499355 is 553994773
• Previous prime number is 83

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 52
• Digital Root 7

### Name

Name one billion four hundred seventy-nine million nine hundred twenty-seven thousand seven hundred twenty-eight

### Interesting facts

• 1479927728 has 128 divisors, whose sum is 7664896512
• The reverse of 1479927728 is 8277299741
• Previous prime number is 727

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 56
• Digital Root 2

### Name

Name one billion nine hundred six million six hundred eighty thousand nine hundred eighty-eight

### Interesting facts

• 1906680988 has 8 divisors, whose sum is 4290032232
• The reverse of 1906680988 is 8890866091
• Previous prime number is 2

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 55
• Digital Root 1