An arctic village maintains a circular crosscountry ski trai

An arctic village maintains a circular cross-country ski trail that has a radius of 2 kilometers. A skier started skiing from the position (0.141, 1.995), measured in kilometers, and skied counter-clockwise for 2 kilometers, where he paused for a brief rest. (Consider the circle to be centered at the origin). Determine the ordered pair (in both kilometers and radii) on the coordinate axes that identifies the location where the skier rested. (Hint: Start by drawing a diagram to represent this situation.) (x,y) = ( ) radii (z, y) = ( *) kilometers

Solution

The circumference of the trail is C = 2(pi)r = 12.6 km.
If the skier skis clockwise 2.0 km, they have traversed 57.3 degrees.

west of south, at a distance of 2.0 km from the origin.
Thus their position would be (-2.0*sin(57.3), -2.0cos(57.3)) km = (-1.37, -1.46).
In radius lengths, that is just (-sin(57.3), -cos(57.3))