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Soros Olympiad in Mathematics
I Soros Olympiad 1994-95 (Rus + Ukr)
11.2
sin x <= sin (x+1)<=. ..<= sin (x+4) (I Soros Olympiad 1994-99 Round 2 11.2)
sin x <= sin (x+1)<=. ..<= sin (x+4) (I Soros Olympiad 1994-99 Round 2 11.2)
Source:
May 26, 2024
algebra
inequalities
trigonometry
Problem Statement
Find the smallest positive
x
x
x
for which holds the inequality
sin
x
≤
sin
(
x
+
1
)
≤
sin
(
x
+
2
)
≤
s
i
n
(
x
+
3
)
≤
sin
(
x
+
4
)
.
\sin x \le \sin (x+1)\le \sin (x+2)\le sin (x+3)\le \sin (x+4) .
sin
x
≤
sin
(
x
+
1
)
≤
sin
(
x
+
2
)
≤
s
in
(
x
+
3
)
≤
sin
(
x
+
4
)
.
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