we just started polar coordinates.
I do not understand graphically how the length of archimedes spiral is equal to the angle.
For example if the point under consideration is $(\frac{\pi}{2},\frac{\pi}{2})$. I'm confused on how $\frac{\pi}{2}$ can be a tangible length for the $r$ value. like if it was $(1, \frac{\pi}{2})$ i know that its the length of $1$ at angle $\frac{\pi}{2}$ but how can $\frac{\pi}{2}$ be an actual number?
Thanks.
You are talking about the curve defined by the set of all ordered pairs $(\theta, r)$ such that $r = \theta$, and $\theta$ is measured in radians. It should be easy to see that if the angle is $\theta$, and $r$ has to match $\theta$, then we first angle ourselves from the positive $x$-axis up to $\theta$, and then march outwards in the radial direction a distance $\theta$. After all, $\theta$ is a number. You may be overthinking this.