Arab Academy for Science, Technology & Maritime Transport
Mathematics I
BA 121

Spring 2011
Solving simultaneous linear equations ( two
variables ) :
Consider the following linear system of the two unknowns x
and y
a11 x + a12 y = b1 ,
a21 x + a22 y = b 2
Solving this system , is to find the values of x and y which
satisfy that system. We apply
Arab Academy for Science, Technology & Maritime Transport
Mathematics I
BA 121

Spring 2011
Properties of spherical triangle :
1. If a circle is drawn on a sphere
so that the radius of the circle is
the same as the radius of the
sphere it is called a great circle .
Any other circle is a small circle
.
2. An infinit number of great circle
can pas
Arab Academy for Science, Technology & Maritime Transport
Mathematics I
BA 121

Spring 2011
Trigonometric functions :
hypetenous
opposite
x
adjacent
opposite
hypetenous
sin x opposite
=
tan x =
cos x adjacent
adjacent
hypetenous
1
cos x adjacent
=
=
& cot x =
tan x sin x opposite
sin x =
& cos x =
1
cos x
sec x =
& cos ec x =
1
sin x
Note that :
Arab Academy for Science, Technology & Maritime Transport
Mathematics I
BA 121

Spring 2011
Solving quadrantal spherical triangle :
In case giving a spherical triangle in which one side is 90 , we use
the following fundamental rules ,
sin m iddle = tan( adj .) tan ( adj .)
sin m iddle = cos(opp .) cos (opp .)
Example :
1. Solve the following rig
Arab Academy for Science, Technology & Maritime Transport
Mathematics I
BA 121

Spring 2011
Solving oblique spherical triangle :
Cases :
1. in case knowing three a , b , c , sides , we use the haversine
formula
havA =
hav a hav (c b)
sin c . sin b
and similarly for B and C
2. Using the sine formula
sin A sin B sin C
=
=
sin a sin b sin c
3. in c
Arab Academy for Science, Technology & Maritime Transport
Mathematics I
BA 121

Spring 2011
Differentiation
1. Basic Rules
d n
x = nx n 1
dx
d
k =0
dx
d
( ) = uv ' u 'v
uv
+
dx
d u
u 'v v 'u
( )=
dx v
v2
d n
u = nu n 1u '
dx
d
cos(u ) = sin(u ).u '
dx
d
sin(u ) = cos(u ).u '
dx
d
tan(u ) = sec 2 (u ).u '
dx
d
cot(u ) = cos ec 2 (u ).u '
dx
d
sec
Arab Academy for Science, Technology & Maritime Transport
Mathematics I
BA 121

Fall 2015
COLLEGE OF ENGINEERING & TECHNOLOGY
Department : Basic and Applied Sciences
Lecturer: Math. Staff
Course : Mathematics 1
Course No. : BA 110
Marks: 40
Date : 3/1/2014
Time : 9.00 11.00 (2Hours)
:
4)
B
B (4, 1)
A (2, 3)
.A
(
(. i
A
Solution:
y y1 y2