1985 AHSME Problems/Problem 10: Difference between revisions

Revision as of 13:27, 26 November 2011

Problem

An arbitrary circle can intersect the graph $y=\sin x$ in

$\mathrm{(A) } \text{at most }2\text{ points} \qquad \mathrm{(B) }\text{at most }4\text{ points} \qquad \mathrm{(C) } \text{at most }6\text{ points} \qquad \mathrm{(D) } \text{at most }8\text{ points}\qquad \mathrm{(E) }\text{more than }16\text{ points}$

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 $y=0$ , which intersects $y=\sin x$ 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, $\boxed{\text{E}}$ .

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

Page

Toolbox

Search

1985 AHSME Problems/Problem 10: Difference between revisions

Revision as of 13:27, 26 November 2011

Problem

Solution

See Also