What is the misconception about the polar equation of a hyperbola at theta = pi?

[RadiationX]

I think that I'm over looking something with this problem. Below is the equation of an hyperbola in polar form.

$$R=\frac{1}{1 + 2cos{\theta}}$$

when $$\theta =\pi$$ shouldn't $$R = -1$$? And not $$R= 1$$
Am I over looking some property of the $$\cos$$ function?
Even when i evalute this expression at $$\theta=\pi$$in my ti-89 i get that R is = to 1. What am i not seeing?

 

[bahamut]

You have made a mistake,im afraid.
Even if you find that R=-1,it is just a mathmatic form.
R is always positive,you can just say R=|1/2cos(theta)|
If still don't understand,contact me at wangkehandsome@hotmail.com,I will be glad to anwser it for you and even be more glad if you point out my fallacy.

 

[Data]

Well, then he hasn't made a mistake: the given expression is just wrong!

 

[RadiationX]

I see the error. Both of you are correct. the expression is not explicit enough. when i plot these points in the xy plane they are (-1,0) BUT the same coordinates in the
$$(r,\theta)$$ coordinate system are $$(1,\pi)$$ because the radius is always positive