# How do you graph #r = 1 + 2 sin(3theta) #?

##### 1 Answer

Dec 1, 2016

See the graphs and the explanation.

#### Explanation:

The period for

Max r = 3 and min r = 0.

In half period #theta -n [-pi/18, 5/18pi], the whole loop is drawn. In the

other half

The first graph is locally zoomed at the pole to reveal the dimple

therein. The second reveals the loop representing the whole

periodic curve, redrawn periodically, with period

graph{(x^2+y^2)(x^2+y^2-sqrt(x^2+y^2)-6y)-8y^3=0 [-2.5, 2.5, -1.25, 1.25]}

graph{(x^2+y^2)(x^2+y^2-sqrt(x^2+y^2)-6y)-8y^3=0 [-80, 80, -40, 40]}