Question

How do you graph `r=3sintheta+3`?

Answer 1

The family of cardioids through the pole r = 0 is given by

`r = a ( 1+cos (theta-alpha))`.

Here parameter a gives the maximum reach from the pole as 2a..

`alpha` is the second parameter. The line `theta=alpha` gives

the line of symmetry.

The whole cardioid can be traced for one period `2pi`, for example

`theta in (alpha, alpha+2pi)`,, .

Here,`r = 3(1+ cos (theta-pi/2)`, and so, #a = 3 and theta=alpha =

pi/2#. So, the size is 6 units and the line of symmetry is

perpendicular to the initial line.

The half of this cardioid in `Q_4 and Q_1` can be traced, using

`(r, theta): (0, 3/2pi) (3-13sqrt2, 7/4pi) (3, 0) (3+3/sqrt2, pi/4) (6, pi/2)`.

The other half in `Q_2 and Q_3` can be drawn as mirror image,

with respect to the line of symmetry, `theta = pi/2`.