# How do you graph #r=3+sin(5theta)#?

##### 1 Answer

See 5 loops of

#### Explanation:

Make the graph for one period

repeat in a cycle of period

Use this Table to get the wave-like curve for one period. ..

The graph for

around the circle r = 3.

Indeed, interesting.

Analogy: The path of either pole on the Earth's surface with a

compound period of about 256 centuries, for its precession, is

similar ( but complicated) on the surface of our Earth. The radius of

this circle is about 2535 km.

Graph of #r = 3 + sin 5theta and the circle around which this

twines#:

graph{((x^2+y^2)^3-3(x^2+y^2)^2.5-5 x^4y+10x^2y^3-y^5)(x^2+y^2-9)=0 [-8 8 -4 4]}

Graph of 12 waves twining around a circle in

graph{((x^2+y^2)^6.5-3(x^2+y^2)^6-12 (x^11y-xy^11)+220(x^9y^3-x^3y^9)-792(x^7y^5-x^5y^7))(x^2+y^2-9)=0 [-8 8 -4.2 4.2]}