(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

"Consider the graph of [itex]r = e^{\theta}[/itex] in polar coordinates. Then consider the graph of [itex](\theta \cos{\theta}, \theta \sin{\theta})[/itex] where [itex]\theta \in \mathbb{R}[/itex] on the Cartesian plane (x - y axis). How are the two graphs related? What relationship (if any) can we define between [itex]e^{\theta}[/itex] and the trigonometric functions?

3. The attempt at a solution

What I considered was [itex]r^2 = x^2 + y^2[/itex] where [itex]x = \theta \cos{\theta}[/itex] and y = [itex]\theta \sin{\theta}[/itex]. Plugging this all in I get:

[tex] e^{2\theta} = (\theta)^2 ((\cos{\theta})^2 + (\sin{\theta})^2) [/tex]

which reduces to:

[tex] e^{2 \theta} = (\theta)^2 [/tex]

taking the ln of both sides, noting that [itex]\theta \ne 0[/itex]:

[tex] 2 \theta = 2 ln \theta [/tex]

[tex] \theta = ln \theta [/tex]

So as it stands now, the above equation has no real solutions. So I thought maybe putting each side as a power of e would be the relation between the two graphs.

[tex] e^{\theta} = e^{ln \theta} [/tex]

[tex] e^{\theta} = {\theta} [/tex]

which is kind of a circluar argument because I just rearranged the equation. They mention this has something to do with trigonometric functions, I'm not seeing the connection. I would apprectiate some help.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Polar Coordinates Problem

**Physics Forums | Science Articles, Homework Help, Discussion**