Graph y=(1/2)tan(x)

Graph y=(1/2)tan(x)
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 tangent function, , for equal to to find where the vertical asymptote occurs for .
Set the inside of the tangent 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.
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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 .
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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 .
Divide by .
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:
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 one billion four hundred eleven million seventy-two thousand three hundred thirty-five

Interesting facts

  • 1411072335 has 16 divisors, whose sum is 1803395232
  • The reverse of 1411072335 is 5332701141
  • Previous prime number is 17

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 27
  • Digital Root 9

Name

Name one billion two hundred forty-nine million eight hundred forty-eight thousand three hundred sixty-seven

Interesting facts

  • 1249848367 has 4 divisors, whose sum is 1315629880
  • The reverse of 1249848367 is 7638489421
  • Previous prime number is 19

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 52
  • Digital Root 7

Name

Name one billion seven hundred twenty-four million nine hundred ninety-two thousand four hundred sixty-nine

Interesting facts

  • 1724992469 has 4 divisors, whose sum is 1727610720
  • The reverse of 1724992469 is 9642994271
  • Previous prime number is 659

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 53
  • Digital Root 8