Question

Thanks for helping! This question is really weird :(

r=-6sin theta

I need to multiply both sides of the equation by r and use r^2=x^2+y^2 to rewrite the equation in terms of x and y.

Answer 1

@Ashleyisakitty @jim_thompson5910 @zepdrix @Nnesha @e.mccormick @wio @sammixboo @kropot72 @mathmate

Answer 2

Ok so you want to convert it to rectangular, it's good you notice we have to multiply r and use \[r^2 = x^2+y^2\] we know the ratio for sin theta is the following \[\sin \theta = \frac{ y }{ r }\] so we have \[r = - 6\left( \frac{ y }{ r } \right)\] can you finish it off?

Answer 3

I'm not sure I understand where to go from there

Answer 4

\[r^2 = - 6y\]

Answer 5

What's next?

Answer 6

square - 6y?

Answer 7

Why? Look at what we know, and we want to "get rid" of the polar coordinates.

Answer 8

x^2?

Answer 9

I don't know what that means

Answer 10

add it in?

Answer 11

Hint: \[r^2 = x^2+y^2\]

Answer 12

-6y=x^2+y^2?

Answer 13

Yes, that looks good :)

Answer 14

You can rearrange it and what not if you wish

Answer 15

That is it in terms of x and y?

Answer 16

I'm asked to complete the square to produce another equation in my worksheet. Should I do it from this form?

Answer 17

You may complete the square

Answer 18

Ah, yes we have to complete the square, you know how to do that right?

Answer 19

When you have it as such \[-6y=x^2+y^2 \] it's always best to complete the square as it will be in terms of x and y.

Answer 20

I know how to do it in regular form, but I'm sort of confused about this one

Answer 21

\[-6y = x^2+y^2 \implies x^2+y^2 + 6y = 0\]

Answer 22

Oh, I thought it was when you added (b/2)^2 to both sides or something like that

Answer 23

I didn't complete the square...I put in a form so you can complete the square.

Answer 24

Oh, okay gotcha

Answer 25

So we don't need to worry about the x^2, now complete the square for y^2+6y

Answer 26

When you have \[x^2+ax \implies x^2+ 2 \frac{ ax }{ 2 } + \left( \frac{ a }{ 2 } \right)^2-\left( \frac{ a }{ 2 } \right)^2\] to complete the square.

Answer 27

Wouldn't that make it remain the same?

Answer 28

Sorry, I suck at pre calc :(

Answer 29

You should try it, otherwise me doing everything is not going to help you :P

Answer 30

very true

Answer 31

But when plugging in y^2+6y in, it cancels back to y^2+6y, no?

Answer 32

Mhm, no you don't do that, we don't plug in anything I just put if you have the form y^2+6y you do the following -> .....etc

Answer 33

\[x^2+ax \implies x^2+ 2 \frac{ ax }{ 2 } + \left( \frac{ a }{ 2 } \right)^2-\left( \frac{ a }{ 2 } \right)^2\]
\[x^2+ ax \implies y^2+6y\] in your question

Answer 34

y ^2+6x+9-9?

Answer 35

wait, no

Answer 36

now we just factor