+279 Convert \(r = {7 \over 9sinθ-cosθ}\) to rectangular form.
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\(y = { [] \over []} x + \frac{[]}{[]}\)
Hello:) I'm trying to convert the polar equation above into a rectangular equation. I looked up a Youtube video to do it and I got stuck after a certain point.
Here's my work:
1) I multiplied r on both sides.
\(r^2 = {7 \over 9sinθ - cosθ} \times r\)
2) Because r2 equals x2 + y2 , I substituted x2 + y2 into r2.
\(x^2 + y^2= {7 \over 9sinθ-cosθ}\times r\)
For the next part, I'm confused, because it says that cosθr is equal to x. And because the r is being multiplied at the end, I'm tripped up lol so if someone could help me understand the next step, I'd appreciate that so much!
+500 I'm not sure about the approach you took, but have you tried multiplying both sides by the denominator(\(9\sin{\theta}-\cos{\theta}\)) from the beginning? Maybe that would get you somewhere, since you know that \(r * \cos{\theta} = x \) and \(r * \sin{\theta} = y\)
Not sure if you're asking for the solution, but if you are, then you can keep reading I guess.
Using the method mentioned above:
\(9r\sin{\theta} - r\cos{\theta} = 7\)
Using our substitutions, we rewrite this as:
\(9y - x = 7\)
From here on out, it gets pretty intuitive. Dividing and rearranging to get our desired form, we get:
\(9y = x+7\)
\(y = x/9 + 7/9\)
or
\(y = \frac19 x + \frac79\)
Hope this helped!
