Graph y=cot(4x-pi/2)-3

Graph y=cot(4x-pi/2)-3
Find the asymptotes.
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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 .
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Add to both sides of the equation.
Divide each term by and simplify.
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Divide each term in by .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Multiply .
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Multiply and .
Multiply by .
Set the inside of the cotangent function equal to .
Solve for .
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Move all terms not containing to the right side of the equation.
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Add to 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.
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Move to the left of .
Add and .
Divide each term by and simplify.
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Divide each term in by .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Multiply .
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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.
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 .
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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 .
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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:
Multiply the numerator by the reciprocal of the denominator.
Phase Shift:
Multiply .
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Multiply and .
Phase Shift:
Multiply by .
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 two hundred twenty-nine million nine hundred fifty-one thousand eight hundred forty-three

Interesting facts

  • 1229951843 has 4 divisors, whose sum is 1230039408
  • The reverse of 1229951843 is 3481599221
  • Previous prime number is 69991

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 44
  • Digital Root 8

Name

Name two hundred eleven million seventy-four thousand seven hundred eighty-two

Interesting facts

  • 211074782 has 8 divisors, whose sum is 316677000
  • The reverse of 211074782 is 287470112
  • Previous prime number is 14149

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 32
  • Digital Root 5

Name

Name one billion six hundred eighty-eight million one hundred thirty-five thousand five hundred fifty-two

Interesting facts

  • 1688135552 has 512 divisors, whose sum is 28990224648
  • The reverse of 1688135552 is 2555318861
  • Previous prime number is 197

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 44
  • Digital Root 8