Question

Convert the polar equation r=4sinθ to a Cartesian equation.
Answer choices:
x^2 + y^2 = 4y
x^2 + y^2 = 4x

Answer 1

Hello again! We're you able to make sense of that other document that had been given? :)

Answer 2

Kind of, but I was still a little confused.

Answer 3

OK. Well let me give you a summary of key things you need to know to solve these sort of problems.

Answer 4

Ok!

Answer 5

\[r = \sqrt{x^2+y^2}\] \[\cos(\theta) = \frac{x}{r}\] \[\sin(\theta) = \frac{y}{r}\]

Answer 6

Those are the three most important facts you need to know. The question is... how to use them?

Answer 7

ok

Answer 8

It's a good idea to convert the trig functions first. They are kind of annoying anyways. Let's start by changing the sin into something else.

Answer 9

Let's write down the change as:
\[r = 4 \sin \theta\] becomes
\[r = 4 \cdot (\frac{y}{r})\]
Does that make sense so far?

Answer 10

yes it does

Answer 11

Perfect! Now, if you wanted you could switch out the r's now. You would get a bit of a mess though. I'm going to be a little tricky and multiply both sides by r, to get the r's by themself.

Answer 12

\[r = 4 \cdot (\frac{y}{r})\] becomes \[r^2 = 4y\]

Answer 13

ok

Answer 14

Now this is a wonderful equation to have! Remember that r is a square root of x^2 and y^2. But since we now have r^2 the square root goes away! Like this...

Answer 15

\[r^2 = 4y\] becomes \[(\sqrt{x^2+y^2})^2 = 4y\] which is easy \[x^2 + y^2 = 4y\]

Answer 16

Thank you so much it makes a lot more sense now! :)

Answer 17

Glad to help! Just remember, convert trig first, then see if you can make an r^2 (they are friendly), then convert r and you are done! :)

Answer 18

Thanks!