Page 661 - APPLIED PROCESS DESIGN FOR CHEMICAL AND PETROCHEMICAL PLANTS, Volume 1, 3rd Edition

A-24. A-24.

( Continued). ( Continued).
TRICONOMETRIC FORMULAS PROPERTIES OF SECTIONS

Radlu1 AF - 1
TRIGONOMETRIC • 1in• A+ co1• A » 1in A coaec A SQUARE
FUNCTIONS • co• A sec A - tan A cot A Axis of n,omenh through center A di
1
Sine A • COi A• _,_ -co• A tan Ae ..J1-co1 A• BC d
cot A col8eA "t 0 - 2
c
- 1 -
Cosine A - eln A. • aln A cot A• V1-ain 1 A • AC ----- __ _l
aecA
tanA
Tangent A • sin A = - 1 - • aln A aeo A • FD
co1 A cot A s d•
COi A 1 6
Cotangent A • sin A unA • coa A eesee A • HG
=
d-- d
tan A 1 r ..J12 • .288675 d
Secant A - ain A - cos A • AD
cot A 1 --------------------··
Coaecant A • coaA • ain A • AG
.. -----�--��------- -.,=�=m�==��- SQUARE
RIGHT ANGLED Axia of moment, on baH A di
TRIANGLES a1 1:11 c• -bl c d
b• - c.• -a• d•
cl • a• +bl l .. -4---t-- .1 T
>
- -��-�-·--- -- ---�-=----- 8 T "O
di
"O
d
::,
Known Required r ..J"i - ,177360 d CD
A B • b c Aro a d Q.
;c
b ab
•• b tan A• f tan B = - ..J a•+ bl 2
a
a, c aln A• � coa B • � vc•-=-:i•· a ..Jc•- a•
0 2 SQUARE
a a• cot A
A, a 90°-A a cot A iinA --2- Axis of momenta on diagonal
b b• tan A • ,707107 d
A,b 90°-A b tan A coaA -- 2 -
c 1 sin 2 A d•
A,c 90° -A c sin A c coa A 4 12
di
S • &,/2 • ,117851 d•
a• • b• + c• - 2 be coa A
a+b+c d
• - --2-- bl - a• + c• - 2 ac cos B r v12 • .288675 d
c• • a• + bl - 2 ab coa C

Required RECTANGLE
Known A bd
A B c b 0 Area Axia of moment, through center
1 1 e d
a, b, c co,!.A • coa 2 B � coa c • "' • <•-•> (a-b) (a-o) 2
2
2
c
ci·-_,.-, � .<•-bi � · (a-c) _______ j_ bd•
� bo ac ab 12
a sin B a1in C bdl
a, A, B 180°-<A+B> -iTnA ,inA 8 T
b sin C
d
a, b, A sin B• ball!!- ---.ma r vl2 • ,2Ht75 d
a
CJ)
a 1in C ab sin C I>- ....
a, b,C tan A• l>-a coa C ..J a•+b•-2ab co• C -2-- I,)