(a) Use the addition formulas for sin and cos to prove that tan ( π / 2 − x ) = 1 / tan x . (b) Show that ( 0 , π / 4 ) can be used as a fundamental domain for tan x . (c) Design a tangent key, following the principles of Program 3.3, using degree 3 polynomial interpolation on this fundamental domain. (d) Empirically calculate the maximum error of the tangent key in ( 0 , π / 4 ) .
(a) Use the addition formulas for sin and cos to prove that tan ( π / 2 − x ) = 1 / tan x . (b) Show that ( 0 , π / 4 ) can be used as a fundamental domain for tan x . (c) Design a tangent key, following the principles of Program 3.3, using degree 3 polynomial interpolation on this fundamental domain. (d) Empirically calculate the maximum error of the tangent key in ( 0 , π / 4 ) .
Solution Summary: The author explains that in trigonometry, the following equations are valid: l=mathrmsin
(a) Use the addition formulas for
sin
and
cos
to prove that
tan
(
π
/
2
−
x
)
=
1
/
tan
x
. (b) Show that
(
0
,
π
/
4
)
can be used as a fundamental domain for
tan
x
. (c) Design a tangent key, following the principles of Program 3.3, using degree 3 polynomial interpolation on this fundamental domain. (d) Empirically calculate the maximum error of the tangent key in
(
0
,
π
/
4
)
.
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