Page 54 - Aeronautical Engineer Data Book

Fundamental dimensions and units 41

t
� f(x)dx F(s)/s
0
d n F
n
(–t) f(t) 3 3
s d n
at
e f(t) F(s – a)
f(t – a)H(t – a) e –as F(s)
d n f n
n
3 3 s F(s) – � s n–r (r–1) (0+)
f
t d n r=1
1 1
3 3 e –bt sin at, a > 0 33
2
a (s=b) + a 2
s + b
e –bt cos at 33
2
(s+ b ) + a 2
1 1
3 3 e –bt sinh at, a > 0 33
2
a (s+b) + a 2
s + b
e –bt cosh at 33
2
(s+ b) + a 2
(πt) –1/2 s –1/2
n n–1/2
2 t
33, s –(n+1/2)
�
1·3·5...(2n –1)�π
n integer
ex p(– a 2 /
t)
4
3 3 (a > 0) e –a � s �
3
t
2(π ) 1/2
2.8.14 Basic trigonometry
Definitions (see Figure 2.9)
y x
3
sine: sin A = 3 3 cosine: cos A = 3
r r
y x
3
tangent: tan A = 3 3 cotangent: cot A = 3
x y
r r
secant: sec A = 3 3 cosecant: cosec A = 3 3
x y