# Graph y=1/4*sec(x)

Graph y=1/4*sec(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 secant function, , for equal to to find where the vertical asymptote occurs for .
Set the inside of the secant 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. Vertical asymptotes occur every half period.
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. This is half of the period.
There are only vertical asymptotes for secant and cosecant 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 seven million nine hundred sixty thousand nine hundred six

### Interesting facts

• 507960906 has 8 divisors, whose sum is 1015921824
• The reverse of 507960906 is 609069705
• Previous prime number is 3

### Basic properties

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

### Name

Name two billion twenty-seven million one hundred fifty-three thousand fifty-five

### Interesting facts

• 2027153055 has 8 divisors, whose sum is 2169941760
• The reverse of 2027153055 is 5503517202
• Previous prime number is 283

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 30
• Digital Root 3

### Name

Name one billion five hundred nine million six hundred eighty-seven thousand nine hundred forty-five

### Interesting facts

• 1509687945 has 32 divisors, whose sum is 3331728000
• The reverse of 1509687945 is 5497869051
• Previous prime number is 29

### Basic properties

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