January 2014
Intermediate to advanced
144 pages
4h 2m
English
Content preview from Mathematical Formulas for Industrial and Mechanical Engineering
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Product to Sum
sin u sin v 5
1
2
ðcosðu2 vÞ2 cosðu1 vÞÞ cos u cos v5
1
2
ðcosðu2 vÞ1 cosðu 1 vÞÞ
sin u cos v 5
1
2
ðsinðu1 vÞ1 sinðu 2 vÞÞ cos u sin v5
1
2
ðsin ðu1 vÞ2 sin ðu2 vÞÞ
Sum to Product
sin u1 sin v5 2 sin
u1v
2
cos
u2v
2
sin u2 sin v5 2 cos
u1 v
2
sin
u2 v
2
cos u1 cos v5 2 cos
u1 v
2
cos
u2v
2
cos u2 cos v52 2 sin
u1v
2
sin
u2v
2
Power Reducing Identities
sin
2
u 5
1 2 cosð2uÞ
2
cos
2
u 5
1 1 cosð2uÞ
2
tan
2
u 5
1 2 cosð2uÞ
1 1 cosð2uÞ
sin
2
u 5
1 2 cosð2uÞ
2
sin
3
u 5
3 sin u 2 sin 3u
4
cos
3
u 5
cos 3u 1 3 cos u
4
4.8 The Inverse Trigonometric Functions
Arc Sine
Let f :½2π=2; π=2!½21 ; 1 where f(x) 5 sin x. Therefore, its inverse function is
defined by f
21
:½21; 1 !½2π=2; π=2,whe
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