Question

Convert the equation to polar form.
5x=5y

AND

x^2+y^2=16

Answer 1

x=r cosƟ, y=r sinƟ, x^2+y^2=r^2.

Answer 2

I don't get the second one. x^2+y^2=r^2

Answer 3

No, not really. Trig and I don't get along at all

Answer 4

ok loco do you have that picture i drawed you where I graph (x,y) and called the angle between the initial ray and I guess we can call it the vector with endpoints at the origin and at the point (x,y)

Answer 5

yeah, it's open in my pdf

Answer 6

k and I put inside a circle i called the radius of that circle r

Answer 7

that trangle is a right triangle so we can use Pythagorean them to find what r is in terms of x and y

Answer 8

r=sqrt(x^2+y^2)

Answer 9

or like anwar said before x^2+y^2=r^2

Answer 10

yeah, i don't this equation? what do i use it for?

Answer 11

we want to convert x^2+y^2=16 to a polar equation so that means we want it in terms of r and pheta
but what is x^2+y^2=.....?

Answer 12

loco, do you know what to fill that blank with?

Answer 13

5x^2+5y^2=16

Answer 14

if we are doing 5x^2+5y^2=16
then we can factor out 5 so we have 5(x^2+y^2)=16
but what does x^2+y^2=----?

Answer 15

does it equal r?

Answer 16

right!

Answer 17

sorry, if i take too long, trying to figure this out

Answer 18

5r=16 is the polar equation of the cartesian equation 5x^2+5y^2=16

Answer 19

these equations give the same graph using a little different way of graphing

Answer 20

these are equations are equivalent

Answer 21

polar is in the form (r,pheta)
Cartesian is in the form (x,y)

Answer 22

what do u mean equivalent? = to what? 16

Answer 23

no to each other

Answer 24

so 5x=5y, is that what u mean?

Answer 25

5r=16 is equivalent to 5x^2+5y^2=16 because they are the same graph

Answer 26

oh ok...

Answer 27

so you want to convert 5x=5y to polar equation?

Answer 28

yes

Answer 29

so remember polar has (r,pheta) form
so x=rcos(pheta) and y=rsin(pheta)
5rcos(pheta)=5rsin(pheta) we could divide both sides by 5
so we have
rcos(pheta)=rsin(pheta)
rcos(pheta)-rsin(pheta)=0
r(cos(pheta)-sin(pheta))=0
so we have r=0 and cos(pheta)-sin(pheta)=0

Answer 30

wow... um.. let me try to figure all this out

Answer 31

ok

Answer 32

There?

Answer 33

hey i was talking to my hubby. hes gonna be home soon so I'm going to leave soon but we were done with writing 5x=5y to a polar equation

Answer 34

yes

Answer 35

so did you have a question or something?

Answer 36

this might sound arrogant but, how do i set it up and how do i get the answer

Answer 37

how you have to do is place x^2+y^2 with r and replace x with rcos(pheta) and y with rsin(pheta) and usually I tried to simplified like I did above

Answer 38

all not how

Answer 39

write with no x and no y

Answer 40

your goal is to write with r and pheta

Answer 41

ok

Answer 42

x^2+y^2 with r^2*

Answer 43

do you see my mistake way up there?
i forgot r^2 when i wrote 5r^2=16 is equivalent to 5x^2+5y^2=16

Answer 44

so it would be 5^2+5^2=

Answer 45

?

Answer 46

where did you get x=5 and y=5?

Answer 47

oh.. crap. i got them from the original equation

Answer 48

hey anwar is going to come back and help you i have to leave k?

Answer 49

ok thank you very much for all ur help though :)

Answer 50

i think you are over thinking this stuff

Answer 51

i tend to do that a lot :P

Answer 52

i hope you get it

Answer 53

thank you

Answer 54

i got the whole night, don't worry i'll get it

Answer 55

Just gimme a minute. I'll help you when I finish with another question if you still need help.

Answer 56

ok

Answer 57

I don't know where you have reached. But I'll start by these formula in polar coordinates:
\[x=r \cos \theta .... (1)\]
\[y=r \sin \theta .... (2)\]
\[x^2+y^2=r^2 .... (3)\]

Answer 58

We're trying to convert the given equations that are in terms of x and y to an a form in terms of r and theta, which is called polar coordinates. Is that clear so far?

Answer 59

Good, Now consider the first equation: 5x=5y. Divide both sides by 5 you get:
\[x=y\] But we can substitute fot x with equation (1) and for y with equation (2). That's:
\[x=y \implies r \cos \theta=r \sin \theta\]

Answer 60

ok

Answer 61

Is is clear so far?

Answer 62

Is it*

Answer 63

For the 2nd equation:
\[x^2+y^2=16\]
we will just apply directly the third formula, since x^2+y^2 is just r^2. Then:
\[x^2+y^2=16 \implies r^2=16\]

Answer 64

is this the answer

Answer 65

Yep. You can simplify it more, but this is OK.