3
votes
3answers
814 views

How can I find the points of intersection between the curves $r=1+\sin\theta$ and $r=1-\sin\theta$?

Find the points of intersection for the curve $r=a(1+\sin\theta)$ and $r=a(1-\sin\theta)$ My book says the answer is $(0,0),(a,0),(a,\pi)$. However I calculated $ (a,0),(a,\pi),(a,2\pi)$.
2
votes
2answers
136 views

Self-intersection of vector valued function

A vector valued function $r(t)$ has the following coordinates: $$x = 4\cos\left(\frac12t\right)+2\cos(2t)+\cos(4t)\\ y = 4\sin\left(\frac12t\right)+2\sin(2t)+\sin(4t)$$ I have to find the $t$-values ...
4
votes
0answers
370 views

Calculating equidistant points around an ellipse arc

As an extension to this question on equiangular fisheye distortion, how can I calculate equidistant points around an ellipse (or 1/4 segment of) given it's aspect ratio? When it's circular, I can use ...
0
votes
1answer
118 views

Prove if a polar function involves only the rational numbers and sin, cos, tan functions, it can be written in rectangular form.

Prove if a function only have including the rational numbers and sin, cos, tan function and $r$, you always could write it in rectangular form. Ex. For $r=2/(2+2\cos\theta)$ it could be represent in ...
1
vote
1answer
230 views

polar graphs and investigation

I am new to polar graphs and I am trying to investigate some certain cases: What happens when you change the $b$ value to different positive integers in polar equations of the forms: ...
3
votes
3answers
2k views

Writing a Polar Equation for the Graph of an Implicit Cartesian Equation

If $(x^2+y^2)^3=4x^2y^2,$ then $r=\sin 2\theta$ for some $\theta$. Using $r^2=x^2+y^2, x=r\cos\theta,y=r\sin\theta$, it's easy to get $r^2=\sin^22\theta$. But I don't know what to do next, since ...
1
vote
2answers
833 views

Express this curve in the rectangular form

Express the curve $r = 9/(4+\sin \theta)$ in rectangular form. And what is the rectangular form? if I get the expression in rectangular form, how am I able to convert it back to polar ...