Math CentralQuandaries & Queries


Question from srishti, a student:

Consider the points P= (-sin(a-b),-cosa), Q=(cos(a-b),sina), R=(cos(a-b+c),sin(a-c), where 0<b,
a< π/4, then what is the relation between this points? As in, either they are collinear or non-collinear.

I wonder if there might be some typographical error in the statement of your problem. Simply assign a fixed value to a and to b. Then P and Q will be fixed points which determine a fixed line. If you replace c by the variable x then R is a an oval-shaped curve, so you can be certain that for most choices of a, b, and c, the points will not be collinear. (Also, since b never appears alone, you can simplify the way the problem looks by replacing a-b everywhere with d.)


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