# Graph -cot(x)

Graph -cot(x)
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 .
Set the inside of the cotangent function equal to .
The basic period for will occur at , where and are vertical asymptotes.
Find the period to find where the vertical asymptotes exist.
The absolute value is the distance between a number and zero. The distance between and is .
Divide by .
The vertical asymptotes for occur at , , and every , where is an integer.
There are only vertical asymptotes for tangent and cotangent functions.
Vertical Asymptotes: for any integer
No Horizontal Asymptotes
No Oblique Asymptotes
Vertical Asymptotes: for any integer
No Horizontal Asymptotes
No Oblique Asymptotes
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 .
Divide by .
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: for any integer
Amplitude: None
Period:
Phase Shift: ( to the right)
Vertical Shift:
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### Name

Name three hundred seventeen million six hundred seventy-seven thousand two hundred eighty-four

### Interesting facts

• 317677284 has 32 divisors, whose sum is 806052960
• The reverse of 317677284 is 482776713
• Previous prime number is 67

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 45
• Digital Root 9

### Name

Name eight hundred fifty-seven million six hundred sixty-three thousand twenty-two

### Interesting facts

• 857663022 has 16 divisors, whose sum is 1816227792
• The reverse of 857663022 is 220366758
• Previous prime number is 17

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 39
• Digital Root 3

### Name

Name one billion two hundred seventy-four million six hundred eighty-eight thousand one hundred ninety-eight

### Interesting facts

• 1274688198 has 32 divisors, whose sum is 2709500640
• The reverse of 1274688198 is 8918864721
• Previous prime number is 3

### Basic properties

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