# Thread: Confusing polar coordinates

1. ## Confusing polar coordinates

Find Cartesian coordinates for all points of intersection of the curves given below:
r=1-sin(theta) and r^2=4sin(theta)
Sketch these.

I am not sure how to do this. Do you square the r=1-sin(theta) and set it equal to 4 sin (theta) and solve for theta? That seems complicated. What is the best approach?

2. Originally Posted by twittytwitter
Find Cartesian coordinates for all points of intersection of the curves given below:
r=1-sin(theta) and r^2=4sin(theta)
Sketch these.

I am not sure how to do this. Do you square the r=1-sin(theta) and set it equal to 4 sin (theta) and solve for theta? That seems complicated. What is the best approach?

$(1-sin\theta)^2=r^2=4sin\theta$

$1-6sin\theta+sin^{2}\theta=0$

$(sin\theta-3)^{2}-9+1=0$

$(sin\theta-3)^{2}=8$

$sin\theta-3=\pm{\sqrt{8}}$

$sin\theta=3\pm{2\sqrt{2}}$

Since, $sin\theta\leq{1}\Rightarrow{sin\theta=3-2\sqrt{2}}$

$sin\theta=3-2\sqrt{2}$

This value satisfies both the given equations.

Therefore, $\theta=n\pi+(-1)^{n}sin^{-1}(3-2\sqrt{2})$ ; where $n\in{Z}$

Hope this helps.

3. thank you