Question

find the cartesian equation of r = 8 sin thet + 8 cos theta

Answer 1

its a circle centered at the irigin of radius 8 maybe?

Answer 2

\[r =\sqrt{x ^{2}+y ^{2}}\]

Answer 3

polars and parametrics aint my strong point ;)

Answer 4

youre good at vectors :)

Answer 5

yep, I can point at things all day lol

Answer 6

haha, and good at planes

Answer 7

maybe youre good at visualizing things?

Answer 8

im pretty good at visualizing stuff

Answer 9

ok we can use x = r cos theta, and y = r sin theta,

Answer 10

so multiply both sides by r

Answer 11

spinning polars tho.....not so much; aint had the practice

Answer 12

\[\sin \theta =x/r\]

Answer 13

ive read the vector stuff, it just wont stick. for some reason

Answer 14

polars are just vector equations at heart :)

Answer 15

i dont see that

Answer 16

r = magnitude; <cos,sin> are the components

Answer 17

r<cos(t),sin(t)> is the basi set up

Answer 18

those are the cartesian components you mean

Answer 19

in the plane, yes

Answer 20

but polars define length(r) whih is the magnitude of a vector; and the <cos,sin> angles are the x and y components of a vector

Answer 21

a vector function simply defines a curve or surface generated by the parametric equations for the vector components from teh origin

Answer 22

and that is all a polar equation is

Answer 23

come again, parametric equation for the vector components (the cartesian components?)

Answer 24

(r,t) is a polar equation right? (radius,theta)

this tells you how far to turn and how far to move

Answer 25

thats all a vector is; an arrow indicating direction and length

Answer 26

ok , lets use th for theta

Answer 27

ok , so say again your statement

Answer 28

which one lol

Answer 29

r<cos(th),sin(th)> is the vector equivalent of a polar equation (r,th)

Answer 30

or simpy <r cos(th), r sin(th)>

Answer 31

vector , as in the cartesian components of the vector

Answer 32

yes

Answer 33

the point P(x,y) is the same as defining a vector from the origin as <x,y>

Answer 34

the vector is an arrow pointing to the point

Answer 35

right, that sometimes confuses me

Answer 36

we write < x,y> for a vector, and P(x,y) for a point

Answer 37

sometimes they write a vector as v(x,y) which confuses tha tmatter; i prefer the convention of just making it pointy to indicate its an arrow :)

Answer 38

right, i like to distinguish between points (n tuples) and vectors

Answer 39

cantorset i posted a proof for your viewing sorry it took me awhile to respond

Answer 40

i cant find it, one sec

Answer 41

k