Engineering Fundamentals: An Introduction to Engineering, 4th ed.c

The cosine rule:

Some other useful trignometry identities:

cos 1 a 2 cos a

sin 1 a 2 sin a

cos 2acos

2

asin

2

a2 cos

2

a 1  1 2 sin

2

a

sin 2a2 sin a cos a

sin

2

acos

2

a 1

c

2

a

2

b

2

 2 ba 1 cos u 2

b

2

a

2

c

2

 2 ac 1 cos b 2

a

2

b

2

c

2

 2 bc 1 cos a 2

u

S 1

R 1



S 2

R 2

cos 1 ab 2 cos a cos bsin a sin b

cos 1 ab 2 cos a cos bsin a sin b

sin 1 ab 2 sin a cos bsin b cos a

sin 1 ab 2 sin a cos bsin b cos a

686 Appendix

Some Useful Mathematical Relationships

loglogarithm to the base 10 1 common logarithm 2

x

n



1

x

n^

x

n

x

mx

nm

a

x

y

b

n



x

n

y

n

1 x

n

2

m

x

nm

x

0

 1 1 x 02

x

n

x

m

x

nm

1 xy 2

n

x

n

y

n

1 degree

p

180

0.0174533 rad

1 radian

180

p

57.2958°

2 p360 degrees

p3.14159p

ln x 1 ln 10 21 log x 2 2.302585 log x

e

x

y ln yx

lnlogarithm to the base e 1 natural logarithm 2

e2.71828p

log x

n

n log x

log

x

y

log xlog y

log xylog xlog y

log 10 1 log 100 2 log 1000 3

10

x

y log yx log 1 0

Some Useful Area Formulas

Triangle A

1

2

bh Rectangle

h

b

Abh

h

b

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