Question

Convert the polar equation to rectangular from:

r= 3sec theta / 5 sec theta +5

Answer 1

please note that I can write your equation as below:
\[r=\frac{ 3 }{ 5 }\frac{ \cos(\theta+5) }{ \cos \theta } \]

Answer 2

Okay, that makes sense.

Answer 3

so we have:
\[\frac{ 5 }{ 3 }r=\cos 5-\tan \theta \sin 5\]
do you agree?
@IronWalrus

Answer 4

I don't understand how you got the right side of the equal sign. Can you explain that?

Answer 5

because:
\[\frac{ \cos(\theta+5) }{ \cos \theta }=\frac{ \cos \theta \cos 5-\sin \theta \sin 5 }{ \cos \theta }\]
\[=\cos5-\tan \theta \sin 5\]

Answer 6

do you agree? @IronWalrus