Shouldn't the graph of r Sin(t) = Sin (r Cos(t))

r=(Sin (r*Cos (t)))/(Sin (t) )

give me the same thing as y=f(x)=Sin (x) which is the Sine Curve?

Yes, I believe this is correct.

jsnc wrote:

I tried entering as a polar equation "r(t)=", and then as a relation.

How does one graph the Sine function as a polar equation?\

I don't think that is possible. Unfortunately Graph cannot plot polar functions as relations. I might add support for that one day. And I don't think it is possible to isolate r in the equation, so I think you have to use cartesian coordinates to plot y=sin(x).

jsnc wrote:

Why do you indicate the Polar Coordiantes as (θ, r) instead of (r, θ)?

Where do I do that? I cannot seem to find anywhere I do that, though it sounds like something I might do.

jsnc wrote:

Continuing on, I can graph the relation (x-3)^2 + (y-2)^2=4

A circle with center (3, 2) and radius 2

But after converting this to a Polar Equation 13/(2(3cos(t))+(2Sin(t))) I get a straight line?

Well, it looks like you didn't convert it correctly. The polar coordinates for the center is:

r0=sqrt(13), t0=atan(2/3), a=2

The generic formula for a circle in polar coordinates is:

r(t) = r0*cos(t-t0) + sqrt(a^2-r0^2*sin(t-t0)^2)

I have attached a file that is showing this.

]]>r=(Sin (r*Cos (t)))/(Sin (t) )

give me the same thing as y=f(x)=Sin (x) which is the Sine Curve?

y = r Sin(t)

x = r Cos(t) substitute into x,y equation

I tried entering as a polar equation "r(t)=", and then as a relation.

How does one graph the Sine function as a polar equation?\

r(t) - 1+Cos(t) Cardioid graphed just fine.

Why do you indicate the Polar Coordiantes as (θ, r) instead of (r, θ)?

Continuing on, I can graph the relation (x-3)^2 + (y-2)^2=4

A circle with center (3, 2) and radius 2

But after converting this to a Polar Equation 13/(2(3cos(t))+(2Sin(t))) I get a straight line?

Continuing on, I believe that the graph of the equation (4(sin(t))^2+9(cos(t))^2)^.5 should match the graph of the Parametric Equation: 2sin(t), 3cos(t) (I converted the Parametric to the Polar), but it doesn't.

I added my Graph file for both Parametrics and Polar.