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Thread: 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 $\displaystyle \sin(x)$ and $\displaystyle \cos(x)$. You can then apply transformations as with any graph.

    For example the graph of $\displaystyle y = \sin \left(x+\frac{\pi}{6}\right) $ is the same shape as $\displaystyle y=\sin(x)$ but moved by $\displaystyle \frac{\pi}{6}$ 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 $\displaystyle {\pi}$, it will cross it in point $\displaystyle \frac{\pi}{3}$ 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 $\displaystyle 5{\pi}$?

    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 $\displaystyle {\pi}$, it will cross it in point $\displaystyle \frac{\pi}{3}$ 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 $\displaystyle 5{\pi}$?

    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 $\displaystyle \sin(x)$ and the second based on $\displaystyle \cos(x)$

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

    Spoiler:
    $\displaystyle \sin(x) = \cos \left(x - \frac{\pi}{2}\right)$. This can also be shown by using the trig addition formulae
    Last edited by e^(i*pi); Apr 10th 2010 at 07:31 AM. Reason: see post
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