# Graph y=5cot(4x)

Graph y=5cot(4x)
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 forty-three million eight hundred seven thousand five hundred eighty-eight

### Interesting facts

• 1043807588 has 8 divisors, whose sum is 2348567082
• The reverse of 1043807588 is 8857083401
• Previous prime number is 2

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 44
• Digital Root 8

### Name

Name one billion twenty-five million seven hundred one thousand two hundred seventy-eight

### Interesting facts

• 1025701278 has 64 divisors, whose sum is 2425835520
• The reverse of 1025701278 is 8721075201
• Previous prime number is 1229

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 33
• Digital Root 6

### Name

Name one billion one hundred ninety-three million eight hundred ten thousand eight hundred thirty-two

### Interesting facts

• 1193810832 has 128 divisors, whose sum is 6309358272
• The reverse of 1193810832 is 2380183911
• Previous prime number is 151

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 36
• Digital Root 9