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Math Help - Please Help... trig functions and graphs

  1. #1
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    Exclamation Please Help... trig functions and graphs

    Please I need help with these questions!

    1. tell the amplitude, horizontal shift and vertical shift of
    y = 2*cos(3x - pi/2) + 4
    2. Find the exact value of the vertical asymptotes for 0<x<pi for the function
    y = cot(3x)
    3. List the exact amplitude, period and horizontal shift for
    y = 2*tan(pi*x + 3)
    4. Identif all vertical asymptotes for 0<x<2pi
    y = tan(2x - pi/4)

    Thank you so much!
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  2. #2
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    1. after you factor it should be
    2cos 3(x-30) + 4

    so the amp is 2, horizontal shift is 30 units right, vertical shift is 4 units up

    sorry for the lack of help lol
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  3. #3
    Amy
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    hope following link will be helpful

    trigonometry
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by cuteisa89 View Post
    Please I need help with these questions!

    1. tell the amplitude, horizontal shift and vertical shift of
    y = 2*cos(3x - pi/2) + 4
    2. Find the exact value of the vertical asymptotes for 0<x<pi for the function
    y = cot(3x)
    3. List the exact amplitude, period and horizontal shift for
    y = 2*tan(pi*x + 3)
    4. Identif all vertical asymptotes for 0<x<2pi
    y = tan(2x - pi/4)

    Thank you so much!
    Iamdenis' response will help you to do problem 3 as well. Here's how to approach problems 2 and 4

    we have a vertical asymptote when we attain x-values for which the function is undefined. since x cannot be such values, the graph will approach the line but never touch it. so all we have to do for questions 2 and 4 is find values of x where the function is undefined in the specified limits. i shall demonstrate with 2, try 4 on your own.

    2. cot(3x) = cos(3x)/sin(3x)
    this function is undefined where sin(3x) = 0

    for vertical asymptotes:
    sin(3x) = 0
    => 3x = arcsin(0)
    => 3x = 0 + kpi for k an integer
    => x = 0 + k*pi/3 for k an integer
    => x = pi/3 and 2pi/3 for 0 < x < pi ........these lines form vertical asymptotes

    the following posts may also help:

    http://www.mathhelpforum.com/math-he...functions.html

    http://www.mathhelpforum.com/math-he...ase-shift.html
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