# Solve for x in Radians cos(2x)+cos(x)=0

Solve for x in Radians cos(2x)+cos(x)=0
Use the double-angle identity to transform to .
Factor by grouping.
Reorder terms.
For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .
Multiply by .
Rewrite as plus
Apply the distributive property.
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
Factor out the greatest common factor (GCF) from each group.
Factor the polynomial by factoring out the greatest common factor, .
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Set equal to and solve for .
Set equal to .
Solve for .
Add to both sides of the equation.
Divide each term in by and simplify.
Divide each term in by .
Simplify the left side.
Cancel the common factor of .
Cancel the common factor.
Divide by .
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.
Simplify .
To write as a fraction with a common denominator, multiply by .
Combine fractions.
Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply by .
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 radians in both directions.
, for any integer
, for any integer
, for any integer
Set equal to and solve for .
Set equal to .
Solve for .
Subtract from both sides of the equation.
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 radians in both directions.
, for any integer
, for any integer
, for any integer
The final solution is all the values that make true.
, for any integer
, for any integer
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### Name

Name eight hundred eighteen million nine hundred sixty-eight thousand eight hundred forty-eight

### Interesting facts

• 818968848 has 64 divisors, whose sum is 5528040048
• The reverse of 818968848 is 848869818
• Previous prime number is 3

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 60
• Digital Root 6

### Name

Name three hundred seventy-one million three hundred eleven thousand sixty-five

### Interesting facts

• 371311065 has 8 divisors, whose sum is 528086912
• The reverse of 371311065 is 560113173
• Previous prime number is 3

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 27
• Digital Root 9

### Name

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

### Interesting facts

• 1202981774 has 4 divisors, whose sum is 1804472664
• The reverse of 1202981774 is 4771892021
• Previous prime number is 2

### Basic properties

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