anonymous
  • anonymous
Convert the polar equation to rectangular form and identify the graph. r= 7/ (2cosΘ+5sinΘ)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
|dw:1393722700861:dw|
anonymous
  • anonymous
y = r sin(theta) x = r cos(theta) x^2 + y^2 = r^2 plug and chug
anonymous
  • anonymous
yea so how would i plug it in

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anonymous
  • anonymous
cuz i did this last week and i kinda forgot sorry
myininaya
  • myininaya
Try getting your cos and sin with r over there by multiplying both sides by 2cos(theta)+5sin(theta)
anonymous
  • anonymous
okay. i did that
myininaya
  • myininaya
So you have: \[2rcos(\theta)+5rsin(\theta)=7 ?\]
anonymous
  • anonymous
why would you put r w/ each one of the terms isnt there just 1?
myininaya
  • myininaya
\[r=\frac{7}{2\cos(\theta)+5 \sin(\theta)} => r(2\cos(\theta)+5 \sin(\theta))=7\] Distributive property!
anonymous
  • anonymous
oh ok i gotchu
myininaya
  • myininaya
you should have it from here. Use the equations sour gave you.
anonymous
  • anonymous
thannk you(:
anonymous
  • anonymous
what if the question's like r= -3sinΘ ?
myininaya
  • myininaya
Try multiplying r on both sides recall rsin(theta)=y and r^2=x^2+y^2
anonymous
  • anonymous
hmm ok...
anonymous
  • anonymous
so r^2= -3rsinΘ?
myininaya
  • myininaya
right so now you are able to replace rsin(theta) with y and r^2 with x^2+y^2
anonymous
  • anonymous
okay
anonymous
  • anonymous
then youd have?
anonymous
  • anonymous
the square root of that right?
myininaya
  • myininaya
just do exactly what I said replace r sin(theta) with y replace r^2 with x^2+y^2
anonymous
  • anonymous
i did tht
myininaya
  • myininaya
you are done what else do you want?
anonymous
  • anonymous
is tht my final answer
anonymous
  • anonymous
oh ok
myininaya
  • myininaya
putting an equation in terms of just x and y ( or just x or just y) is called a cartesian equation if that was the directions to just right as a cartesian equation then you are done
myininaya
  • myininaya
write*
anonymous
  • anonymous
right, sorry. i missed a problem on my homework it was r= 2sinΘ-4cosΘ
myininaya
  • myininaya
multiply both sides by r
anonymous
  • anonymous
do you square both sides 1st
anonymous
  • anonymous
thts what i emant
myininaya
  • myininaya
replace r^2 with x^2+y^2 replace r sin(theta) with y replace r cos(theta) with x
anonymous
  • anonymous
ok i did that: x^2+y^2= 2y-4x
myininaya
  • myininaya
yep. :) that is right you wrote the poloar equation as a cartesian equation if that is all the directions said to do then you are done.
anonymous
  • anonymous
do you stop there
anonymous
  • anonymous
ok
anonymous
  • anonymous
aand i missed r= 3+3cosΘ
anonymous
  • anonymous
so i multiplied both sides by r 1st
anonymous
  • anonymous
and got x^2+y^2=3r +3x but dont i need to get rid of the r?
myininaya
  • myininaya
you could subtract both sides by 3x giving you \[x^2+y^2-3x=3r \] then square both sides and replace the r^2 with x^2+y^2
anonymous
  • anonymous
why square both sides?
myininaya
  • myininaya
I just prefer my answer without radicals and me squaring both sides will allow me to write my answer without radicals
anonymous
  • anonymous
so what would be final answer then
myininaya
  • myininaya
what if you with what I was saying take my equation and then square both sides and then replace the r^2 with x^2+y^2 you will have your final answer
anonymous
  • anonymous
yeah but when you square the whole left side you get x^4+y^4-9x^2 = 3x^2+y^2?
myininaya
  • myininaya
\[(x^2+y^2-3x)^2=(3r)^2 \] the us what you get when you square both sides your equation is not equivalent to that you squared each term sorta but not really it is whatever you do to one side of equation you can do to the other and the equation still holds
myininaya
  • myininaya
\[\text {recall law of exponents} (3r)^2=3^2r^2=9r^2=9(x^2+y^2) \]
anonymous
  • anonymous
so..
anonymous
  • anonymous
im not following are you saying keep left side just squared in parentheses?
myininaya
  • myininaya
It is easier than multiplying it out, don't you think?
anonymous
  • anonymous
yes. so only change right side. like substitue
myininaya
  • myininaya
You can multiply it out if you want. Just do it correctly, but the if the directions just say write as a rectangular (aka cartesian equation) than you are done. If the left hand side was already in terms of x and y. r^2 was the only thing that needed to be converted.

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