Question

I'm so confused
Transform this to rectangular form
rcsc(θ)=5

Answer 1

rewrite as \[\frac{r}{\sin(\theta)}=5\] as a first step

Answer 2

then \[r=5\sin(\theta)\]
now replace \(\sin(\theta)\) by \(\frac{y}{r}\)

Answer 3

if i lost you yet, let me know
only two more steps

Answer 4

This is my first time trying these so they are quite confusing to me hehe. But I am pretty sure I am following. You are replacing sin(theta) with y/r because of the equation y=rsin(theta) right?

Answer 5

rigth

Answer 6

so now we are at \[r=\frac{y}{r}\]right ?

Answer 7

oh no wrong \[r=\frac{5y}{r}\] forgot the 5

Answer 8

Okay, yes, I see :)

Answer 9

Here's how I did it. See the attached image. Either way, you'll get the same answer.

Answer 10

yeah same thing
next would be \[r^2=5y\] and \[x^2+y^2=5y\]

Answer 11

Thank you so much both of you!! Can you help me with one more @satellite73

Answer 12

sure why not (if i can)

Answer 13

Haha! \[r=(4/2\cos \theta-3\sin \theta)\]

Answer 14

btw it might have been easier to replace \(\sin(\theta)\) byu \(\frac{y}{r}\)right away to get \[\frac{r^2}{y}=5\]in one step
so you have lots of choices

Answer 15

\[r=\frac{4}{2\cos(\theta)-3\sin(\theta)}\]

Answer 16

Yes, that's it

Answer 17

i think it is a line
in any case put \(\cos(\theta)=\frac{x}{r}\) and \(\sin(\theta)=\frac{y}{r}\) and do a bunch of agebra

Answer 18

\[r=\frac{4}{\frac{2x}{r}-\frac{3y}{r}}\]

Answer 19

That makes sense!

Answer 20

i would actually flip that sucker to make it less painful \[\frac{1}{r}=\frac{\frac{2x}{r}-\frac{3y}{r}}{4}\]

Answer 21

now multiply both sides by \(r\)
you ca see they will go bye bye

Answer 22

Oh! Wow, that's amazing haha! And then just multiply by 4?

Answer 23

yeah i guess

Answer 24

you get something like \[4=2x-3y\] right?

Answer 25

That's what I got :)

Answer 26

Thank you so so much!

Answer 27

yw