# Graph y=-cot(4x-pi)

Graph y=-cot(4x-pi)
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 .
Solve for .
Add to both sides of the equation.
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Set the inside of the cotangent function equal to .
Solve for .
Move all terms not containing to the right side of the equation.
Add to both sides of the equation.
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
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:
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 three hundred eighty-two million five hundred thirteen thousand six hundred fifty-five

### Interesting facts

• 1382513655 has 16 divisors, whose sum is 1485993600
• The reverse of 1382513655 is 5563152831
• Previous prime number is 233

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 39
• Digital Root 3

### Name

Name one billion seventy-one million three hundred five thousand eight hundred ten

### Interesting facts

• 1071305810 has 32 divisors, whose sum is 1982724912
• The reverse of 1071305810 is 0185031701
• Previous prime number is 277

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 26
• Digital Root 8

### Name

Name seven hundred sixty-nine million two hundred seventy-one thousand five hundred twenty-three

### Interesting facts

• 769271523 has 4 divisors, whose sum is 1025695368
• The reverse of 769271523 is 325172967
• Previous prime number is 3

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 42
• Digital Root 6