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2
2009 Calculus #2: Nested Sines and Cosines
2009 Calculus #2: Nested Sines and Cosines
Source:
June 23, 2012
calculus
trigonometry
function
integration
Problem Statement
The differentiable function
F
:
R
→
R
F:\mathbb{R}\to\mathbb{R}
F
:
R
→
R
satisfies
F
(
0
)
=
−
1
F(0)=-1
F
(
0
)
=
−
1
and
d
d
x
F
(
x
)
=
sin
(
sin
(
sin
(
sin
(
x
)
)
)
)
⋅
cos
(
sin
(
sin
(
x
)
)
)
⋅
cos
(
sin
(
x
)
)
⋅
cos
(
x
)
.
\dfrac{d}{dx}F(x)=\sin (\sin (\sin (\sin(x))))\cdot \cos( \sin (\sin (x))) \cdot \cos (\sin(x))\cdot\cos(x).
d
x
d
F
(
x
)
=
sin
(
sin
(
sin
(
sin
(
x
))))
⋅
cos
(
sin
(
sin
(
x
)))
⋅
cos
(
sin
(
x
))
⋅
cos
(
x
)
.
Find
F
(
x
)
F(x)
F
(
x
)
as a function of
x
x
x
.
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