+280 Convert r=79sinθ−cosθ to rectangular form.
Enter your answer in slope-intercept form by filling in the boxes. Enter values so that fractions are simplified.
y=[][]x+[][]
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.
r2=79sinθ−cosθ×r
2) Because r2 equals x2 + y2 , I substituted x2 + y2 into r2.
x2+y2=79sinθ−cosθ×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!
+499 I'm not sure about the approach you took, but have you tried multiplying both sides by the denominator(9sinθ−cosθ) from the beginning? Maybe that would get you somewhere, since you know that r∗cosθ=x and r∗sinθ=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:
9rsinθ−rcosθ=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=19x+79
Hope this helped!
