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    I'm only familiar with curve sketching involving trigonometry in polar.. How to draw this? I get that r=0 at theta=pi/2 and pi^2/4 at theta=pi/2 but how do I determine the shape, etc. Do I differentiate dr/dtheta to find the turning point? The mark scheme shows 'Negative gradient at A; Correct form at O.', what does A and O stand for?
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    just plug a few points on your calculator and make a rough sketch.

    then if need be differentiate it to work out turning/inflexion points and mark them on.

    then check what happens when x -> +infinity.

    those are generally the basic steps to sketching a random function (depending on the function you may want to check for asymptotes too)
 
 
 
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