One of the greatest basketball stories in history is immortalized in the movie Hoosiers. Gene Hackman stars as a coach of a men’s basketball team from a tiny high school in the farmlands of Indiana in the 1950s that rose above all odds to win the state basketball championship. Their hometown gymnasium was very small. When the players arrived at the monstrous Hinkle Fieldhouse to play the state championship, they were in awe of the size of the arena. The coach made them measure the dimensions of the court and height of the rim. To their amazement, the measurements were the same as those of their court back home. It was as if their high school court had been picked up and placed in the large arena.
We will do the same thing with right triangles. We will superimpose them onto the Cartesian plane, which will allow us to arrive at a second definition of trigonometric functions in terms of ratios of x- and y-coordinates and distances. This new definition will allow us to find values of trigonometric functions for nonacute angles. Although the Cartesian plane might seem like the Hinkle Fieldhouse, remember that the hometown court (right triangles) lies within it.
IN THIS CHAPTER, we ...
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