How do you graph $r = 3 + 3cosθ$ ?

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Answer 1 · 2016-05-13T16:04:05

Explanation is given below

For graphing this polar curve, it has to be seen, how the value of r behaves as $theta$ goes on increasing. It can be done as follows;

Starting with $theta$ =0 along x axis, r= 6. As $theta$ would increase r would decrease, because $costheta$ would go on decreasing.

At $theta = pi/2$ , r= 3.

As $theta$ would increase further, r would get lesser and lesser and at $theta= pi$ , r=0.

At $theta= (3pi)/2$ , r would be 3 and finally at $theta 2pi$ , r would be 6 again

Having determined the values of r.\, the curve can be sketched as shown below.
enter image source here

How do you graph r = 3 + 3cosθr = 3 + 3cosθ?