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  3. sketch the curve r 1 sin 0 2 h to from solution in

Sketch the curve r 1 sin 0 2 h to from Solution Instead of plotting...

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Calculus

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Sketch the curve r 1 sin 0 2 h to from Solution Instead of plotting points we first sketch the graph of r 1 sin 8 in Cartesian coordinates in the top figure by shifting the sine curve up one unit This enables us to read at a glance the values of r that correspond to increasing values of 0 For instance we see that as r the distance from O increases from 2 increases from 0 to 70 TC 2 so we sketch the corresponding part of the polar curve in figure a As increases from to 7 the top figure shows that r decreases from as shown in part c Finally as 8 increase as shown in part d If we let increase beyond 27 or decrease beyond 0 we would simply retrace our path Putting KIN 37 8 so we sketch the next part of the curve as in figure b As increases from 7 to r decreases from 2 8 2 x 2 8 3T 2 to 27 r increases from together the parts of the curve from figures a d we sketch the complete curve in part e It is called a cardioid because it s shaped like a heart a to to to

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