1. **State the problem:** We are given the equation relating $r$ and $\theta$ as $$r = \frac{1}{\theta}$$ and we want to understand this relationship. 2. **Formula and explanation:** The formula shows that $r$ is the reciprocal of $\theta$. This means as $\theta$ increases, $r$ decreases, and vice versa. Note that $\theta \neq 0$ because division by zero is undefined. 3. **Intermediate work:** - For example, if $\theta = 1$, then $r = \frac{1}{1} = 1$. - If $\theta = 2$, then $r = \frac{1}{2} = 0.5$. - If $\theta = -1$, then $r = \frac{1}{-1} = -1$. 4. **Explanation:** This is a hyperbolic relationship where $r$ and $\theta$ are inversely proportional. The graph will have two branches, one in the first quadrant and one in the third quadrant, approaching the axes but never touching them. **Final answer:** The equation is $$r = \frac{1}{\theta}$$ which describes an inverse relationship between $r$ and $\theta$ with $\theta \neq 0$.