2018 AMC 12A Problems/Problem 9
Contents
Problem
Which of the following describes the largest subset of values of within the closed interval
for which
for every
between
and
, inclusive?
Solution 1
On the interval sine is nonnegative; thus
for all
. The answer is
. (CantonMathGuy)
Solution 2
Expanding as before, Let
,
. We have that
Comparing coefficients of
and
gives a clear solution: both
and
are less than or equal to one, so the coefficients of
and
on the left are less than on the right. Since
, that means that this equality is always satisfied over this interval, or
.
See Also
2018 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 8 |
Followed by Problem 10 |
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All AMC 12 Problems and Solutions |
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