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Math Help - Drawing trigonometrical graphs

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    Drawing trigonometrical graphs

    I need some help with drawing y=sin(x) and y=cos(x) graphs. For example I have y=sin(x + pi/6) and y=cos(3x). How to draw graphs of these trigonometrical functions? How to find out points x and y to draw? I know that first step is finding period of the function. But I don't know how to do that too. So, could someone explain me this?
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    Quote Originally Posted by vykis View Post
    I need some help with drawing y=sin(x) and y=cos(x) graphs. For example I have y=sin(x + pi/6) and y=cos(3x). How to draw graphs of these trigonometrical functions? How to find out points x and y to draw? I know that first step is finding period of the function. But I don't know how to do that too. So, could someone explain me this?
    You must learn the basic shape of \sin(x) and \cos(x). You can then apply transformations as with any graph.

    For example the graph of y = \sin \left(x+\frac{\pi}{6}\right) is the same shape as y=\sin(x) but moved by \frac{\pi}{6} units to the left
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    So if there is y=sin(3x), it means that the graph is three times tightened? I mean that if in y=sin(x) the graph crosses the x-axis in {\pi}, it will cross it in point \frac{\pi}{3} in y=sin(3x)? And for example if there is y=sin(x/5), it means that the graph is five times strained? It will cross x-axis in 5{\pi}?

    And waht about cos? Is the way of drawing it the same?
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    Quote Originally Posted by vykis View Post
    So if there is y=sin(3x), it means that the graph is three times tightened? I mean that if in y=sin(x) the graph crosses the x-axis in {\pi}, it will cross it in point \frac{\pi}{3} in y=sin(3x)? And for example if there is y=sin(x/5), it means that the graph is five times strained? It will cross x-axis in 5{\pi}?

    And waht about cos? Is the way of drawing it the same?
    That's right for the stuff about sin(ax)

    cos(x) is a known graph but the transformations apply equally-for example cos(3x) will also be 3 times tightened


    EDIT: see the attached graphs for how it would look for various transformations - the first one is from \sin(x) and the second based on \cos(x)

    EDIT II: You may notice that the graph of \sin(x) is \frac{\pi}{2} to the right of the graph for \cos(x). Can you deduce a relationship between sin(x) and cos(x) based on this information?

    Spoiler:
     \sin(x) = \cos \left(x - \frac{\pi}{2}\right). This can also be shown by using the trig addition formulae
    Last edited by e^(i*pi); April 10th 2010 at 08:31 AM. Reason: see post
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