A unit-speed plane curve $\gamma$ has the property that its tangent vector $t(s)$ makes a fixed angle $\theta$ with $\gamma(s)$ for all $s$. Show that:
(i) If $\theta = 0$, then $\gamma$ is part of a straight line.
(ii) If $\theta = \pi/2$, then $\gamma$ is a circle.
(iii) If $0 < \theta < \pi/2$, then $\gamma$ is a logarithmic spiral.
I'm stuck on part 3. The hint says to find $k_s=-1/(tan(\theta)s)$ and I have no idea how.
