An arctic village maintains a circular cross-country ski trail that has a radius

Question

An arctic village maintains a circular cross-country ski trail that has a radius of 3.7 kilometers. A skier started skiing from the position (-3.345, 1.581). measured in kilometers, and skied counter-clockwise for 4.07 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. (Start by drawing a diagram to represent this situation.) Points possible: 10 Unlimited attempts. Score on last attempt: 0. Score in gradebook: 0 Message instructor about this question Post this question to forum When you are done, click here to see a summary of your scores.

Explanation / Answer

Circumference = 2pi*R = 2pi*3.7 = 23.25 km

Distance travelled = 4.07 km

If the skier skis counter-clockwise 4.07 km, they have traversed 0.175 of the circle, or 63 degrees

Thus their position would be (3.7*sin63, 3.7*cos63) km

In radii, position would be (sin63, cos63) radii

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