SOLUTION: An arctic village maintains a circular cross-country ski trail that has a radius of 4.5 kilometers. A skier started skiing from the position (4.5,0) and skied counter-clockwise for

Algebra ->  Trigonometry-basics -> SOLUTION: An arctic village maintains a circular cross-country ski trail that has a radius of 4.5 kilometers. A skier started skiing from the position (4.5,0) and skied counter-clockwise for      Log On


   

Question 1003796: An arctic village maintains a circular cross-country ski trail that has a radius of 4.5 kilometers. A skier started skiing from the position (4.5,0) and skied counter-clockwise for 1.8 kilometers before stopping for a rest.
Determine the ordered pair (measured in radius lengths) on the coordinate axes that identifies the location where the skier rested).
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The +1.8+ km is some fraction of the
entire circumference which is:
+2%2Api%2A4.5+ km
----------------
That fraction is:
+1.8+%2F+%28+2%2Api%2A4.5+%29+=+.2%2Fpi+
----------------
The entire circle is +2%2Api+ radians
+%28+.2%2Fpi+%29%2A2%2Api+=+.4+
-----------------
The skier has gone +.4+ radians from ( 4.5,0 )
The x-coordinate is:
+4.5%2Acos%28+.4+%29+=+4.5%2A.921+
+4.5%2A.921+=+4.145+
The y-coorinate is:
+4.5%2Asin%28+.4+%29+=+4.5%2A.389+
+4.5%2A.389+=+1.752+
The skier rested at ( 4.145, 1.752 )
Hope I got it!
( I believe the skier ends up in the 1st quadrant
because +pi%2F4+=+.785+ is greater than +.4+
and that is a 90 degree angle from start )