Solve

R=3(1-sin theta) and graph

1 answer

you can't solve it. It's just a function definition. But, the graph is at

http://www.wolframalpha.com/input/?i=r+%3D+3%281-sin%CE%B8%29

Now, if you want to see its equation in rectangular coordinates,

r = 3 - 3sinθ
r^2 = 3r - 3r sinθ
x^2+y^2 = 3r - 3x
x^2+y^2+3x = 3√(x^2+y^2)
(x^2+y^2+3x)^2 = 9(x^2+y^2)

In general, interesting and simple polar curves have nasty rectangular equations.