# Graph -cot(11x)

Graph -cot(11x)
Find the asymptotes.
For any , vertical asymptotes occur at , where is an integer. Use the basic period for , , to find the vertical asymptotes for . Set the inside of the cotangent function, , for equal to to find where the vertical asymptote occurs for .
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Divide by .
Set the inside of the cotangent function equal to .
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
The basic period for will occur at , where and are vertical asymptotes.
The absolute value is the distance between a number and zero. The distance between and is .
The vertical asymptotes for occur at , , and every , where is an integer.
Cotangent only has vertical asymptotes.
No Horizontal Asymptotes
No Oblique Asymptotes
Vertical Asymptotes: where is an integer
No Horizontal Asymptotes
No Oblique Asymptotes
Vertical Asymptotes: where is an integer
Use the form to find the variables used to find the amplitude, period, phase shift, and vertical shift.
Since the graph of the function does not have a maximum or minimum value, there can be no value for the amplitude.
Amplitude: None
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 .
Find the phase shift using the formula .
The phase shift of the function can be calculated from .
Phase Shift:
Replace the values of and in the equation for phase shift.
Phase Shift:
Divide by .
Phase Shift:
Phase Shift:
Find the vertical shift .
Vertical Shift:
List the properties of the trigonometric function.
Amplitude: None
Period:
Phase Shift: ( to the right)
Vertical Shift:
The trig function can be graphed using the amplitude, period, phase shift, vertical shift, and the points.
Vertical Asymptotes: where is an integer
Amplitude: None
Period:
Phase Shift: ( to the right)
Vertical Shift:
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### Name

Name one billion seven hundred eighty-seven million eight hundred forty-eight thousand ninety-five

### Interesting facts

• 1787848095 has 8 divisors, whose sum is 1904491440
• The reverse of 1787848095 is 5908487871
• Previous prime number is 17

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 57
• Digital Root 3

### Name

Name six hundred forty-three million two hundred thirty-seven thousand seven hundred two

### Interesting facts

• 643237702 has 8 divisors, whose sum is 965010312
• The reverse of 643237702 is 207732346
• Previous prime number is 43931

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 34
• Digital Root 7

### Name

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

### Interesting facts

• 1886377266 has 16 divisors, whose sum is 3309434400
• The reverse of 1886377266 is 6627736881
• Previous prime number is 19

### Basic properties

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