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Math Help - [SOLVED] Trig Function Graphs

  1. #1
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    [SOLVED] Trig Function Graphs

    Hello, I'm new here and this is my first post, but let me get right to the problem.

    I have several functions to graph. Explanations are appreciated, I'm not looking to just get answers.

    1.) y = tan (2 \theta + \pi) + 1

    2.) y = cot ( \theta/2 - \pi/2) - 2

    3.) y = csc \theta + 3

    4.) y = sec ( \theta/3 + \pi) - 1

    Any help is appreciated. Thank you.
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  2. #2
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    #3 isn't clear.

    1) Start with the basic function.
    2) Rewrite to expose the characteristics.
    3) Redraw with one characteristic at a time.

    The first

    y = tan (2( + /2)) + 1

    y = tan (2( - (-/2))) + 1

    y = tan () -- Draw this

    y = tan () -- Draw this. What happens to the PERIOD?

    y = tan (2( - (-/2))) -- Draw this. What happens HORIZONTALLY?

    y = tan (2( - (-/2))) + 1 -- Draw this. What happens VERTICALLY?

    Go for it!
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  3. #3
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    Quote Originally Posted by TKHunny View Post
    #3 isn't clear.
    I am not sure. This is what is written on my paper, but my teacher does make a lot of errors. I apologize.

    As for 1)

    I'm understanding the separation you are doing in the first 2 steps.
    In this step:

    Quote Originally Posted by TKHunny View Post
    y = tan () -- Draw this
    How can I draw the graph if I have no value for \theta?

    I believe i forgot to mention im given a graph with x values ranging from -\pi to \pi
    and y values ranging from 4 down to -2.

    Thank you.

    EDIT: Alright, I think I understand now. I completely forgot the graph of tan \theta for some reason. Too late for my brain heh. Anyway, I got the horizontal shift of - \pi/2 and the + 1 vertical shift. Although I'm not sure about the 2. This is a vertical stretch?
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  4. #4
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    Quote Originally Posted by Heiwa View Post
    Although I'm not sure about the 2. This is a vertical stretch?
    y = tan(x)

    y = b*tan(x) -- Vertical Stretch (b>1)/Shrink(0<b<1)

    y = tan(b*x) -- Horizontal Stretch/Shrink
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  5. #5
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    Oh yes I see now. I actually asked my teacher today. Thanks for the help.
    +thanks.
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