Question

Convert r= 1/ (1+SinƟ) into rectangular coordinates.

Answer 1

rectangular coordinates.<--- or expression?

Answer 2

Directions in the book say "Convert the polar equation to rectangular coordinates."

Answer 3

well... we don't have an angle to use though

Answer 4

I figured that you could multiply both sides by r, which would become r^2= r/ (r+rsinƟ). rsinƟ= y

Answer 5

yes, but that'd give you a "rectangular expression" or "equation", no a coordinate set

Answer 6

I don't need actual numbers. I just have to simplify the equation into terms of x and y

Answer 7

so \(\bf r=\cfrac{1}{1+sin(\theta)}\implies r[1+sin(\theta)]=1\implies r+rsin(\theta)=1\\ \quad \\
{\color{blue}{ r^2=x^2+y^2\implies r=\sqrt{x^2+y^2}\qquad rsin(\theta)=y}}\\ \quad \\
r+rsin(\theta)=1\implies \sqrt{x^2+y^2}+y=1\implies \sqrt{x^2+y^2}=1-y\\ \quad \\
(\sqrt{x^2+y^2})^2=(1-y)^2\)

Answer 8

so.... you'd just expand the binomial on the right-side, and simplify

Answer 9

\[r + r \sin \theta = 1\]
\[r+y = 1\]
\[r^2 = (1-y)^2\]
\[x^2 +y^2 = (1-y)^2\]

Answer 10

jdoe, I understand that you multiplied (1+sinƟ) by r,but how did you get that = to 1?

Answer 11

hmm the 1 was given

Answer 12

\(\bf r=\cfrac{{\color{red}{ 1}}}{1+sin(\theta)}\implies r[1+sin(\theta)]={\color{red}{ 1}}\implies r+rsin(\theta)={\color{red}{ 1}}\)

Answer 13

You cross-multiplied. Woops, my bad.