MathDB
Problems
Contests
International Contests
IMO Longlists
1985 IMO Longlists
12
IMO LongList1985 CAN1-Find the maximum value of sum of sines
IMO LongList1985 CAN1-Find the maximum value of sum of sines
Source:
September 10, 2010
trigonometry
algebra unsolved
algebra
Problem Statement
Find the maximum value of
sin
2
θ
1
+
sin
2
θ
2
+
⋯
+
sin
2
θ
n
\sin^2 \theta_1+\sin^2 \theta_2+\cdots+\sin^2 \theta_n
sin
2
θ
1
+
sin
2
θ
2
+
⋯
+
sin
2
θ
n
subject to the restrictions
0
≤
θ
i
,
θ
1
+
θ
2
+
⋯
+
θ
n
=
π
.
0 \leq \theta_i , \theta_1+\theta_2+\cdots+\theta_n=\pi.
0
≤
θ
i
,
θ
1
+
θ
2
+
⋯
+
θ
n
=
π
.
Back to Problems
View on AoPS