Difference between revisions of "1985 AHSME Problems/Problem 10"
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==Problem== | ==Problem== | ||
| − | An arbitrary [[circle]] can intersect the [[graph]] <math> y=\sin x </math> in | + | An arbitrary [[circle]] can intersect the [[graph]] of <math> y=\sin x </math> in |
| − | <math> \mathrm{(A) | + | <math> \mathrm{(A) \ } \text{at most }2\text{ points} \qquad \mathrm{(B) \ }\text{at most }4\text{ points} \qquad \mathrm{(C) \ } \text{at most }6\text{ points} \qquad \mathrm{(D) \ } \text{at most }8\text{ points}\qquad \mathrm{(E) \ }\text{more than }16\text{ points} </math> |
==Solution== | ==Solution== | ||
Revision as of 00:48, 3 April 2018
Problem
An arbitrary circle can intersect the graph of 
in
Solution
Consider a circle with center on the positive y-axis and that passes through the origin. As the radius of this circle becomes arbitrarily large, its shape near the x-axis becomes very similar to that of 
, which intersects infinitely many times. It therefore becomes obvious that we can pick a radius large enough so that the circle intersects the sinusoid as many times as we wish, 
.
See Also
| 1985 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 9 |
Followed by Problem 11 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
