# Graph 0.5cot(x)

Graph 0.5cot(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 five hundred forty-nine million six hundred forty-six thousand four hundred sixty-three

### Interesting facts

• 549646463 has 4 divisors, whose sum is 549694728
• The reverse of 549646463 is 364646945
• Previous prime number is 18413

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 47
• Digital Root 2

### Name

Name one hundred seventy-eight million five hundred seven thousand seven hundred fifty-two

### Interesting facts

• 178507752 has 32 divisors, whose sum is 614278080
• The reverse of 178507752 is 257705871
• Previous prime number is 51

### Basic properties

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

### Name

Name nine hundred forty-nine million six hundred thirty-two thousand one hundred eleven

### Interesting facts

• 949632111 has 32 divisors, whose sum is 1722539520
• The reverse of 949632111 is 111236949
• Previous prime number is 1277

### Basic properties

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