Question

How do you find the Cartesian equation for r=3sin(theta)?

Answer 1

For the conversion, three relationships may be needed.
sin(theta) = ?/? and cos(theta) = ?/? and r^2 = x^2 + y^2
What goes in the ? fields for sin(theta) and cos(theta)?

Answer 2

@sharone Take a guess. Work with me.

Answer 3

sin(theta)=1
cos(theta)=1
? I know this is more than likely in correct...

Answer 4

@Directrix

Answer 5

incorrect*

Answer 6

sin(theta) = y/r and cos(theta) = x/r and then this: r^2 = x^2 + y^2

Answer 7

r=3sin(theta)
so
r = 3* (y/r) or ( (3y / r) )

r/1 = ( (3y / r) )

That will cross-multiply to give what result?

Answer 8

@Directrix y=r^2/3

Answer 9

That's the same as r^2 = 3y. Right?

Answer 10

Now, we have to get rid of the r.

Answer 11

would you replace the r with r=x/cos(theta)

Answer 12

No because to get to Cartesian, we can have only variables of x and y in this case.
Polar has only r and theta so we have to get rid of those.

Answer 13

Oh wait.. Right, okay..

Answer 14

r^2 = x^2 + y^2 --> Let's use this.

Along with this: r^2 = 3y

Answer 15

x^2+y^2=3y

Answer 16

That would be the answer, right?

Answer 17

r^2 = x^2 + y^2
In place of r^2 in r^2 = 3y, substitute x^2 + y^2 to get
x^2 + y^2 = 3y.

Yes.

Answer 18

Okay. Thank you so so much. You explained so much better than my teacher..

Answer 19

@sharone We might need to leave the equation in y = form. I don't know what is required.

@matricked Thanks for your patience. Come on in to the discussion with us now.

Answer 20

I can do the rest. Solving for the y and such. But thank you so much for your help!

Answer 21

This graph is a circle.