Question

Identify the curve by transforming the given polar equation to rectangular coordinates.

Answer 1

letter (d)

Answer 2

you only need to use below :
\(x = r \cos \theta\)
\(y = r \sin \theta \)

Answer 3

and notice that \(x^2 + y^2 = r^2\)

Answer 4

for #a :

\(r = 2\)

square both sides and replace r^2 by x^2+y^2, you're done.

Answer 5

still kinda unsure how to go about this problem :/

Answer 6

wait I'm sorry, i only need help with letter (d) !

Answer 7

oh you're doing letter d.. okay lol :)

Answer 8

hehe yes! thats the one :)

Answer 9

cross multiply

Answer 10

\[r = \dfrac{6}{3 \cos \theta + 2 \sin \theta}\]

\[r(3 \cos \theta + 2 \sin \theta) =6\]

Answer 11

mk...\[r(3\cos \theta+2\sin \theta)=3\]

Answer 12

oops 6*

Answer 13

distribute \(r\)

Answer 14

let me do that real quick...!

Answer 15

okie

Answer 16

it looks a little weird :S ... let me write it

Answer 17

\[r3\cos \theta+r2\sin \theta=6\]

Answer 18

^?

Answer 19

a*b = b*a

so, r*3 = 3*r

Answer 20

\[r = \dfrac{6}{3 \cos \theta + 2 \sin \theta}\]

\[r(3 \cos \theta + 2 \sin \theta) =6\]

\[ 3~r\cos \theta + 2~r \sin \theta =6\]

Answer 21

thats all? :) @rational

Answer 22

replace rcos and rsin by x and y

Answer 23

\(r\) and \(\theta \) are polar variables, so you're not done until u have them in ur equation

Answer 24

\[r = \dfrac{6}{3 \cos \theta + 2 \sin \theta}\]

\[r(3 \cos \theta + 2 \sin \theta) =6\]

\[ 3~r\cos \theta + 2~r \sin \theta =6\]

\[ 3x+ 2y=6\]

Answer 25

Now you're done. so basically the given polar curve is just a straight line !

Answer 26

you were so helpful! thank you :D

Answer 27

np :)