Chapter 3 - Radian Measure and the Unit Circle - Section 3.3 The Unit Circle and Circular Functions - 3.3 Exercises - Page 125: 87

The length of the shortest arc is 0.9846

We can find the angle $\theta$ in radians: $tan ~\theta = \frac{y}{x}$ $tan ~\theta = \frac{0.83305413}{0.55319149}$ $\theta = tan^{-1}(\frac{0.83305413}{0.55319149})$ $\theta = 0.9846~rad$ The radius is 1. We can find the arc length $S$: $S = \theta~r$ $S = (0.9846~rad)(1)$ $S = 0.9846$ The length of the shortest arc is 0.9846