how do you do r=40/(9sin(theta)+64cos(theta)) into cartesian

Question

lexi724 · Answer

i believe.... r=3.9946

anonymous · Answer

I need to change it so it is in terms of x and y so it needs to be y=something

lexi724 · Answer

Ah... hmm try this site http://www.mathway.com/

tkhunny · Answer

Why not use the usual substitutions?


$x = r\cos(\theta)$
$y = r\sin(\theta)$

$r=40/(9\sin(\theta)+64\cos(\theta))$

$r(9\sin(\theta) + 64\cos(\theta)) = 40$

$9r\sin(\theta) + 64r\cos(\theta) = 40$

You're almost done!

anonymous · Answer

I just realized this about a few minutes ago that you could just cross multiply. so it would be 9x+64y=40

tkhunny · Answer

Three things wrong with that:

1) There should be no such thing as "Cross Multiply".  Forget you ever heard the term.  You certainly did not use that here.  You just used multiplication.

2) You have x and y switched.

3) Very, very subtle, but we changed the Domain.  The Domain of the original is NOT all Real Numbers.  It's probably okay for now, but one day you will need to know this mystery.

anonymous · Answer

of course I mixed up x and y it happens all the time to me. and cross multiply probably was not the right term. Yeah and our teacher told us not to worry about the domain for know. thanks for the help

tkhunny · Answer

Well, there you go.  Covered all three objections in one shot!  Good work.