Question

How do you graph `r = 3 + 3cosθ`?

Answer 1

Explanation is given below

Explanation:

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.