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Mathematics
Problem
The Maclaurin series for
cos
x
\cos x
cos
x
is
1
−
x
2
2
!
+
x
4
4
!
−
x
6
6
!
+
⋯
1-\dfrac{x^{2}}{2!}+\dfrac{x^{4}}{4!}-\dfrac{x^{6}}{6!}+\cdots
1
−
2
!
x
2
+
4
!
x
4
−
6
!
x
6
+
⋯
. What is the least even degree of a Maclaurin polynomial that guarantees the magnitude of the error in approximating
cos
(
1
)
\cos(1)
cos
(
1
)
is less than
10
−
5
10^{-5}
1
0
−
5
? a)
10
10
10
b)
6
6
6
c)
8
8
8
d)
12
12
12
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