Mechanical Engineering Formulas guidelines for ME PDF

Preview

Summary

####### MATH – ECON – ENGG SCIENCEPLANE GEOMETRY Polygons Number of diagonal: Nd = nC 2 – n Interior angle: ( ⁄ ) Area of n-side polygon: side b:( )inscribed in a circle:( )circumscribed in a circle:Circles Arc length:Sector Area:Segment Area: ( )Circle Theorems Inscribed angle (a); Tangent & ch...

Description

MATH – ECON – ENGG SCIENCE PLANE GEOMETRY Polygons Number of diagonal: Nd = nC2 – n Interior angle: ( ⁄ ) Area of n-side polygon: side b: ( ) inscribed in a circle: ( )

circumscribed in a circle:

Cylinder

Rhombus:

( Pyramid

Trapezoid ( ) Trapezium √(

)(

)( )(

√(

( Segment Area: ) Circle Theorems Inscribed angle (a); Tangent & chord (b):  Intersecting chords (c): (  ) ( )( ) ( )( ) Intersecting secants (d): (  ) ( )( ) ( )( ) Tangent and Secant (e): (  ) ( )( ) ( )

)

)(

)(

)

)(

)

= sum of prod. of opposite sides

θ

B

Segment:

Plane Area

Zone: Cone:

ycurve dx  

y2 y1

x curve dy

Pyramid: Torus

A

(d)

C

Triangles )( )

)(

⁄

)

Inscribed in a circle: ⁄

Circumscribes a circle: Circle tangent to side a: ( )

)

(

(

) (

)

)

(e)

) ) )

A

√

√

() () Sine Law

( )

Hexahedron

6

Octahedron

8

A

V

E (F+V-2)

Volume

6

8

12

8

6

12

Dodecahedron 12 12

20

30

= 7.66 3

12

30

= 2.18 3

4 6

20 20

=

2

= =

3

3

2

3

b a

C

B

Napier’s Rule I: Sin-Tan-Ad Napier’s Rule II: Sin-Cos-Op Sine Law

Conoid

3

Cosine Laws: “SPAN”

Volume Circular Disk: V  

Ac cc

b a

180 < A + B + C < 540

Two bases: [ ]

Hyperboloid [ ]

12

c B

Paraboloid

4

Icosahedron

( )

A

Prolate Spheroid major axis

Prismatoid ( ) Regular Polyhedron

4

2

SPHERICAL TRIGONOMETRY

Truncated Prism

Tetrahedron

2

S A T C

O

Oblate Spheroid minor axis

F

R

Tangent Law

Ellipsoid

Regular Polyhedron

y1

Cosine Law

B

θ B

(

A

B

C

( ( (

Lune:

) √( Parabolic segment

SOLID GEOMETRY Prism

C

B A

D θ

H

Wedge:

θ x

θ

TRIGONOMETRY SOH CAH TOA CHO SHA CAO θ

A    ycurve, top  y curve, bottom dx x1 1 2 A   R2 d  2 1

(c)

x2

Frustum of Cone ( ) ( ) Sphere

Ellipse

x2

x1 y2

S   1   y ' dx

Spherical:

x1 x2

V  



 r 2 dy

Propositions of Pappus First Proposition: A  2 R  S Second Theorem: V  2 R  A Length of an Arc

Ptolemy’s theorem:

A

D

Circular Ring:

x1

A  2 3 ab

(b)

A

A

)(

)

s: semiperimeter θ: average of opposite angles

√(

(a)

)(

Cylindrical Shell: V  2  x 2 xy  curve dx

Frustum of a Pyramid ( √ ) Cone

Cyclic Quadrilateral Bramaguptha’s Formula:

Circles Arc length: Sector Area:

√( (

Parallelogram



x2

x1

y curve dx

z

Spherical Coordinates

Spherical Defect, d:

( ) ANALYTIC GEOMETRY Division of Line Segment

ϕ

√

Angle of Inclination

x

yp by MUC,

If m and n are odd,

P(r,θ,ϕ)

𝑓( )

y

θ r

0+ 1

For

n  tan u du or

n  sec u du :

DIFFERENTIAL CALCULUS d  dx d dx d dx d  dx d  dx d  dx

Angle bet. 2 intersecting lines ( )

 

d ax  log a e ax dx d 1 xn  nxn1  ln x  dx x d 1 ex  ex  log a x   log a e dx x d 1 sin 1 x  sin x  cos x dx 1 x 2 d 1 1 cosx   sin x cos x   dx 1  x2 c  0

 

Distance bet. 2 parallel lines

 

√

Distance bet. line and a point √

Area of n-sided polygon

+

* Conic Sections Conics

Eccentricity e  f /d

Discriminant B 2  4 AC

Hyperbola

>1

>0

Parabola

=1

=0

Ellipse...