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 three hundred fifty-two million six hundred eighty-two thousand six hundred eighty-three

Interesting facts

  • 352682683 has 4 divisors, whose sum is 355459840
  • The reverse of 352682683 is 386286253
  • Previous prime number is 127

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 43
  • Digital Root 7

Name

Name seven hundred sixty-eight million nine hundred eighty thousand one hundred seventy

Interesting facts

  • 768980170 has 16 divisors, whose sum is 1581902208
  • The reverse of 768980170 is 071089867
  • Previous prime number is 5

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 46
  • Digital Root 1

Name

Name one hundred forty-two million five hundred seventy-three thousand six hundred eighty-eight

Interesting facts

  • 142573688 has 32 divisors, whose sum is 502107984
  • The reverse of 142573688 is 886375241
  • Previous prime number is 23

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 44
  • Digital Root 8