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    I'm doing fp2 and I'm struggling in sketching polar curves I can do the simple ones okay but the spec is saying I am expected to be able to sketch like 10 different functions, how am I suppose to know what the shape will look like for different types of polar curves does the examiner expect me to know all of them?
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    It's funny cause 2 days ago I was in the same position as you! What I did was watch YouTube videos (Krista King has a few short simple ones) on how they plotted it then created my own notes from that to refer back to. Having a scientific calculator helps as you can put the equation in the "table" function between the limits and it tabulates the results for you to then plot.

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    To give an example of how I do it for the curve r = a(root 2 + 2cos(theta)),
    Assume a = 1. Enter the values of your axes (0, pi/2, pi and 3pi/2) for theta and see what you get. The table function is very useful for this. You plot these and any other theta values will give cos(theta) recognisable values like 1, (root 3)/2 etc. Note, 1 is equivalent to a on your axis, 2 to 2a etc.

    Then think of the shape of the cartesian (non-polar) cos graph. Between 0 and pi/2 it starts at 1 and slopes downward slowly, increasing in speed and it slopes fastest as it approaches 0. The areas where it slopes quickly means a large rotation/change in angle, and vice versa for a gradual slope. So join up your points following that principle. This is better than spending time plotting individual points as the questions typically say "sketch" and aren't worth many marks, at least in my exam board, OCR MEI. I hope this makes sense!



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    There is probably a way to group them.
 
 
 
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