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2011 Kosovo National Mathematical Olympiad
1
KMO #1 (Grade 11) [ f(cosx)=?]
KMO #1 (Grade 11) [ f(cosx)=?]
Source:
March 13, 2011
function
trigonometry
algebra proposed
algebra
Problem Statement
It is given the function
f
:
R
→
R
f:\mathbb{R} \to \mathbb{R}
f
:
R
→
R
such that it holds
f
(
sin
x
)
=
sin
(
2011
x
)
f(\sin x)=\sin (2011x)
f
(
sin
x
)
=
sin
(
2011
x
)
. Find the value of
f
(
cos
x
)
f(\cos x)
f
(
cos
x
)
.
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