# Find the Range y=cos(2x)-1

Find the Range y=cos(2x)-1
Find the magnitude of the trig term by taking the absolute value of the coefficient.
Find the lower bound of the range.
The lower bound of the range for cosine is found by substituting the negative magnitude of the coefficient into the equation.
Subtract from .
Find the upper bound of the range.
The upper bound of the range for cosine is found by substituting the positive magnitude of the coefficient into the equation.
Subtract from .
The range is .
Interval Notation:
Set-Builder Notation:
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### Name

Name one billion seven hundred eighty-four million one hundred thirty-eight thousand four hundred ten

### Interesting facts

• 1784138410 has 32 divisors, whose sum is 3261503232
• The reverse of 1784138410 is 0148314871
• Previous prime number is 71

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 37
• Digital Root 1

### Name

Name one billion seven hundred eighteen million five hundred forty-three thousand eight hundred thirty-six

### Interesting facts

• 1718543836 has 32 divisors, whose sum is 3929627520
• The reverse of 1718543836 is 6383458171
• Previous prime number is 7643

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 46
• Digital Root 1

### Name

Name four hundred seventeen million two hundred forty-six thousand two hundred sixty-eight

### Interesting facts

• 417246268 has 32 divisors, whose sum is 957404448
• The reverse of 417246268 is 862642714
• Previous prime number is 181

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 40
• Digital Root 4