# Graph y=csc(x+(4pi)/5)

Graph y=csc(x+(4pi)/5)
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 cosecant function, , for equal to to find where the vertical asymptote occurs for .
Subtract from both sides of the equation.
Set the inside of the cosecant function equal to .
Move all terms not containing to the right side of the equation.
Subtract from both sides of the equation.
To write as a fraction with a common denominator, multiply by .
Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply by .
Subtract from .
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.
Cosecant 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 .
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 left)
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 left)
Vertical Shift:
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### Name

Name seven hundred ninety-three million two hundred sixty-nine thousand one hundred sixty-six

### Interesting facts

• 793269166 has 8 divisors, whose sum is 1197204264
• The reverse of 793269166 is 661962397
• Previous prime number is 163

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 49
• Digital Root 4

### Name

Name six hundred sixty-eight million eighty-nine thousand eight hundred fifty

### Interesting facts

• 668089850 has 32 divisors, whose sum is 1454450688
• The reverse of 668089850 is 058980866
• Previous prime number is 127

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 50
• Digital Root 5

### Name

Name three hundred fifteen million twenty-nine thousand six hundred eleven

### Interesting facts

• 315029611 has 8 divisors, whose sum is 341346320
• The reverse of 315029611 is 116920513
• Previous prime number is 13

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 28
• Digital Root 1