Question

Convert the rectangular equation to a polar equation. Express r in terms of "theta".

7x-4y=1

Answer 1

@satellite73 @Loser66 please

Answer 2

When converting from rectangular to polar, we can use the fact that:\[\large x=r \cos \theta \qquad \qquad \qquad y=r \sin \theta\]
Sooooo,\[\large 7x-4y=1 \qquad\to\qquad 7r \cos \theta-4r \sin \theta=1\]Factoring an r out of each term gives us,\[\large r(7\cos \theta-4 \sin \theta)=1\]Then to solve for r we simply divide that big messy thing to the other side.
Is this what you're trying to do with this problem? :o

Answer 3

Yes, I think that is what I need to do. Trig confuses me so much.
so:
\[r(7\cos \Theta-4\sin \theta)=1\]
How do I write that in Polar form?

Answer 4

Dividing each side by \(\large 7\cos\theta-4\sin\theta\) gives us,
\[\large r=\frac{1}{7\cos \theta-4\sin \theta}\]
I think this is the polar form they're asking for, with r expressed as a function of theta.
Which is what the instructions were asking for: `Express r in terms of "theta".`

Answer 5

Trig confuses you??? :) Aw man that's my favorite!

Answer 6

Okay thank you! Yeah, it's probably because I did summer trig so it's a little too fast for me. :(

Answer 7

I'm studying for my final right now. so far I have a low B, I'm just trying to keep from getting a C. thank you again for your help!

Answer 8

oh neato c: