# Graph 1/(2cot(2x))

Graph 1/(2cot(2x))
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 tangent 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 .
Multiply .
Multiply and .
Multiply by .
Set the inside of the tangent 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 .
Multiply .
Multiply and .
Multiply 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.
Tangent 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 eighty-five million eight hundred twenty-nine thousand two hundred four

### Interesting facts

• 85829204 has 32 divisors, whose sum is 203993856
• The reverse of 85829204 is 40292858
• Previous prime number is 43

### Basic properties

• Is Prime? no
• Number parity even
• Number length 8
• Sum of Digits 38
• Digital Root 2

### Name

Name ninety-two million nine hundred forty thousand three hundred thirty

### Interesting facts

• 92940330 has 16 divisors, whose sum is 175259304
• The reverse of 92940330 is 03304929
• Previous prime number is 5

### Basic properties

• Is Prime? no
• Number parity even
• Number length 8
• Sum of Digits 30
• Digital Root 3

### Name

Name two billion thirty million five hundred seventy-four thousand seven hundred sixty-seven

### Interesting facts

• 2030574767 has 8 divisors, whose sum is 2237628624
• The reverse of 2030574767 is 7674750302
• Previous prime number is 43

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 41
• Digital Root 5