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16
five cosines are nonpositive
five cosines are nonpositive
Source:
November 15, 2009
trigonometry
Problem Statement
Let
x
x
x
be a real number such that the five numbers
cos
(
2
π
x
)
\cos(2 \pi x)
cos
(
2
π
x
)
,
cos
(
4
π
x
)
\cos(4 \pi x)
cos
(
4
π
x
)
,
cos
(
8
π
x
)
\cos(8 \pi x)
cos
(
8
π
x
)
,
cos
(
16
π
x
)
\cos(16 \pi x)
cos
(
16
π
x
)
, and
cos
(
32
π
x
)
\cos(32 \pi x)
cos
(
32
π
x
)
are all nonpositive. What is the smallest possible positive value of
x
x
x
?
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