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    i'm failing this module on a very big scale, and i dont understand any of the chapter on polar co-ordinates...

    on my homework it says

    draw r=sec(theta-pi/3)

    how do i go about doing this?

    what is r? what is theta?

    could someone talk me through the working?

    similarly, how would i go about drawing r=acos3theta ?

    i dont understand anything
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    Maybe it would help to see how polar coordinates (r and theta) differ from Cartesian coordinates (x and y).

    If you want to plot a graph with Cartesian coordinates, you first make out a table of x and y values. Then you plot each point. To do this, you go along the x axis to the correct x value, then go up to the correct y value. Once you have each point plotted, you join them up.

    With polar coordinates, you make out your table of r and theta, but the process of plotting the coordinates is different. You start at the origin and point towards the positive x axis. Then you rotate anticlockwise by the angle theta (which is in radians). Then you move away from the origin in that direction by the distance r. Then you plot your point. Once you have all the points, you can join them up.

    So let's take your example. You haven't specified the range for theta so I'll assume it's 0 to 2pi.

    Let's start by making a table of values. We'll take theta in intervals of pi/6

    

\begin{array}{c|c} \theta & r \\ \hline

0 & 2 \\

(1/6)\pi & 2/\sqrt{3} \\

(1/3)\pi & 1 \\

(1/2)\pi & 2/\sqrt{3} \\

(2/3)\pi & 2 \\

(5/6)\pi & \mathrm{undefined} \\

\pi & -2 \\

... & ...

\end{array}

    I'll let you fill in the rest.

    Then, you would plot the points as described above. If you get a negative value for r then that represents going in the opposite direction to where you're pointing after rotating theta. If you get 'undefined' then just skip plotting that point. However depending on the range of values you're given for theta, you might not have to worry about these points.



    You should find, if you do this accurately, that your polar graph looks roughly like a straight line.

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    wow thankyou!
 
 
 
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Updated: April 3, 2011

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