# Solve for x cos(x)^2=cos(x)

Solve for x cos(x)^2=cos(x)
Factor out of .
Factor out of .
Factor out of .
Factor out of .
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Set the first factor equal to and solve.
Set the first factor equal to .
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 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 .
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
, for any integer
Set the next factor equal to and solve.
Set the next factor equal to .
Add to both sides of the equation.
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 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.
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
, for any integer
The final solution is all the values that make true.
, for any integer
Consolidate and to .
, for any integer
Consolidate and to .
, for any integer
, for any integer
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### Name

Name one billion four hundred forty-eight million nine hundred sixty-nine thousand ninety-four

### Interesting facts

• 1448969094 has 32 divisors, whose sum is 3221174880
• The reverse of 1448969094 is 4909698441
• Previous prime number is 5081

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 54
• Digital Root 9

### Name

Name one billion three hundred seventy-eight million three hundred eighty-eight thousand seventy-seven

### Interesting facts

• 1378388077 has 4 divisors, whose sum is 1389779836
• The reverse of 1378388077 is 7708838731
• Previous prime number is 121

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 52
• Digital Root 7

### Name

Name three hundred ten million twenty-eight thousand one hundred eighty-eight

### Interesting facts

• 310028188 has 8 divisors, whose sum is 697563432
• The reverse of 310028188 is 881820013
• Previous prime number is 2

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 31
• Digital Root 4