MATHEMATICS
and
CALCULATOR
TECHNIQUES
ENGR. REYNILAN L. DIMAL
THE MEMORY VARIABLES
MEMORY
A
B
C
D
E (ES PLUS only)
F (ES PLUS only)
X
Y
M
CALCULATOR BUTTONS
ALPHA (-)
ALPHA O ‘ “
ALPHA hyp
ALPHA sin
ALPHA cos
ALPHA tan
ALPHA )
ALPHA S D
ALPHA M+
HOW TO CLEAR MEMORY
• SHIFT 9 1 =
– This means you will automatically go to MODE 1
• SHIFT 9 2 =
– All values stored in the memory variables will be
erased
• SHIFT 9 3 =
– This means you will automatically go to MODE 1
and all values stored in the memory variables
will be erased.
MODE 1 :
GENERAL
CALCULATIONS
HOW TO CONVERT BETWEEN
DEGREES, RADIANS AND GRADIANS
Convert237.6150 to DMS (DegreeMin Sec)
DISPLAY:
237.615O
237036'54"
BASICS
HOW TO CONVERT BETWEEN
DEGREES, RADIANS AND GRADIANS
Convert210 47'12"todecimaldegrees.
DISPLAY:
210 470120
21.7866666
7
BASICS
HOW TO CONVERT BETWEEN
DEGREES, RADIANS AND GRADIANS
Convert1200 to radians.
DISPLAY:
1200
2

3
BASICS
HOW TO CONVERT BETWEEN
DEGREES, RADIANS AND GRADIANS
π
Convert radians to degrees.
2
DISPLAY:

r
2
90
BASICS
PAST CE BOARD EXAM
Whatis 1200 in centesimalsystem?
ENTER
DISPLAY:
0
120
400
3
BASICS
HOW TO GET THE POLAR AND
RECTANGULAR COORDINATE OF A
POINT IN THE CARTESIAN PLANE
PAST CE BOARD EXAM
Find thepolarcoordinateof thepoint(4, - 6).
DISPLAY:
Pol(4,6)
r  7.211102551
,  56.30993247
BASICS
HOW TO GET THE POLAR AND
RECTANGULAR COORDINATE OF A
POINT IN THE CARTESIAN PLANE
PAST ECE BOARD EXAM
Find the value of cos if the terminalside
containsthepointP(-3,-4)
Solution :
BASICS
HOW TO GET THE POLAR AND
RECTANGULAR COORDINATE OF A
POINT IN THE CARTESIAN PLANE
PAST ECE BOARD EXAM
DISPLAY:
Pol(3,4)
r  5,  126.8698976
NOT E: r is storedautomatically toX and to Y.
DISPLAY :
cos(Y )
3

5
BASICS
PAST ECE BOARD EXAM
Find therectangular coordinateof a point
whose polarcoordinateis (3,1200 ).
DISPLAY:
Rec(3,120)
X  1.5, Y  2.59807621
BASICS
HOW TO SOLVE COMBINATION
AND PERMUTATION PROBLEMS.
PAST ECE BOARD EXAM
How many triangles are formedby 10 distinct
pointsno threeof which are collinear?
Solution :
T henumber of trianglesthatcan be formedfrom
10 non collinearpointsis 10C3.
DISP LAY:
10C 3
120
BASICS
PAST ECE BOARD EXAM
In how manydifferentways can thejudges choose
the winner and thefirst runner up fromamongthe
10 finalistsin a student essay contest?
Solution :
T hereare10 finaliststaken2 at a time.
Note: order is importanthere
DISP LAY:
10P 2
90
BASICS
HOW TO EVALUATE FACTORIAL
NUMBERS
18. Find the value of 10!
DISP LAY:
10!
3628800
BASICS
PAST EE BOARD EXAM
How manydifferentpermutations can be made
from thelettersMISSISSIP PI?
Solution :
Number of M  1; I's  4; P 's  2; S' s  4;
Number of Lett ers 11.
Note: T henumber of differentpermutations is :
11!
1!4!2!2!
BASICS
PAST EE BOARD EXAM
DISP LAY:
11!
1! x 4! x2!x4!
34650
BASICS
HOW TO EVALUATE
FUNCTIONS
11. Evaluatef( 6 ) if f(x)  3x 4  3x 2-5x  6
BASICS
HOW TO EVALUATE
FUNCTIONS
12. Evaluatef( 4,3 ) if f(x, y)  4x3 y 2  3x 2 y-2xy2  y 3
BASICS
PAST ME BOARD EXAM
Find theremainderwhen 3x4  2x3 - 4x2  x  4 is divided by x  2.
Solution:
f(x)  3x 4  2 x3-4 x 2  x  4 , remainder f(-2 )
BASICS
HOW TO EVALUATE
FUNCTIONS
13. Is (x  3 ) a factorof x6  6x5  8x 4-6x3-9x 2?
Conclusion:Since f(-3) 0,
then x 3 is a factorof
x 6  6 x 5  8 x 4 -6 x 3-9 x 2
BASICS
PAST ECE BOARD EXAM
Find theremainderwhen 4 y3  18y 2  8 y  4 is divided by 2 y  3.
Concept: Set thedivisor tozero and solvefor y.
ENTER :
DISP LAY:
2Y  3  0, Y
- 1.5
ENTER :
DISP LAY:
4Y 3  18Y 2  8Y - 4
11
Answer : T heremainderis 11
ADVANCE
HOW TO USE THE ∑ SIGN
Find the sum. 1  2  3  ...  20
DISP LAY:
20
x
x1
210
BASICS
HOW TO SOLVE LINEAR
EQUATIONS
SOLVE 4(3  x)  5(4  x)
BASICS
HOW TO SOLVE LINEAR
EQUATIONS
x 3
x 1
x2
SOLVE


1
12
6
9
BASICS
HOW TO SOLVE A
SPECIFIC VARIABLE
D
( 2 X  2Y ), X  4, D  2, and A  9,
7
what is the valueof Y ?
If A 
BASICS
PAST ECE BOARD EXAM
When 3 is m ultipliedby 5 less thana num ber,
the result is 9 less than5 tim esthe num ber.
Find 7 less than5 tim esthe num ber.
BASICS
PAST ECE BOARD EXAM
BASICS
HOW TO USE MULTILINE FUNCTION
PAST EE BOARD EXAM
Find thearea of a trianglewhose sides are 6m,8m,12m.
Solution : Using Heron's Formula:
A  s(s - a)(s- b)(s - c)
abc
s
2
ENTER :
BASICS
HOW TO USE MULTILINE FUNCTION
PAST EE BOARD EXAM
DISP LAY:
ABC
X
: X(X - A)(X- B)(X - C)
2
ENTER :
DISP LAY:
X
ABC
2
13
DISP LAY:
X ( X  A)( X  B)( X  C )
455
BASICS
HOW TO SOLVE TRIGONOMETRIC
EQUATIONS
Solve 5tan x - 3  2tan x : 0  x  360
ENTER :
DISPLAY:
ENTER :
5 tan x- 3  2 tan x
X
30
L-R 
0
Answer : X  300 and 2100
DISPLAY:
5 tan x- 3  2 tan x
X
210
L-R 
0
BASICS
HOW TO USE LOGARITHMIC EQUATIONS
PAST ME BOARD EXAM
Solve for xin log2 x  log2 (x  5)  10
ENTER :
DISPLAY:
log2 x  log2 (x  5)  10
X
L-R 
29.5975076
9
0
BASICS
HOW TO USE LOGARITHMIC EQUATIONS
PAST ECE BOARD EXAM
3log x
Solve for xin x
 100x
DISPLAY:
x 3log x  100x
X
L-R 
10
0
BASICS
HOW TO GET THE
DERIVATIVE AT A POINT
Find thederivativeof x3  3x 2 when x  3.
ENTER :
DISP LAY:
d
( X 3  3X 2 )
dx
x 3
45
BASICS
PAST ECE BOARD EXAM
x2
Differentiate theequation y 
x 1
x2  2x
x
a.
b.
c.2 x
2
( x  1)
( x  1)
2x2
d.
( x  1)
T echnique: Differentiate y at any valueof x, say x  2 and comparethis
value to the value of thechoiceswhen same value of x is substituted.
ENTER :
DISP LAY:
d  x2 


dx  x  1  x  2
0.8888888889
ADVANCE
PAST ECE BOARD EXAM
Note: Compareit tothechoicesas thevalueof x is being substituted.
x2  2x
a)
Substitute x  2
2
( x  1)
ENTER :
DISP LAY:
T he valuesof therest of thechoiceswhen x  2
are summarizedas follows:
x2  2x
( x  1) 2
x
2
b.

0.8888888889
( x  1) x 2 3
c.2 xx2  4
x2
4
d .

( x  1) x 2 3
x2  2x
Answer : a.
( x  1) 2
ADVANCE
HOW TO INTEGRATE
2
Evaluate ( x  3x  1)dx
5
1
ENTER :
DISPLAY:
2
x
5
 3x  1 dx
1
16
BASICS
MODE 2 :
COMPLEX NUMBER
CALCULATIONS
HOW TO SOLVE COMPLEX NUMBERS
For thecomplexnumber z  3 - 4i
a. Find theabsolute value.
b. Find theargument.
DISPLAY:
3  4i  r
5  53.13010235
0
Answer : T heabsolute valueis 5 and theargumentis 53.13
BASICS
HOW TO SOLVE COMPLEX NUMBERS
Given : (2 - 3i)(5 2i), find theproduct.
ENTER :
DISP LAY:
(2  3i )(5  2i )
16  11i
BASICS
HOW TO SOLVE COMPLEX NUMBERS
4  2i
Simplify :
5 - 2i
ENTER :
DISPLAY:
4  3i
5  2i
14 23
 i
29 29
BASICS
HOW TO GET THE COMPONENT OF A
FORCE AND RESULTANT OF FORCES
Find thex and y componentsof theforceF  300N370
ENTER :
DISPLAY:
300370
239.590635 180.5445069i
Answer : T hex componentis 239.5N and they componentis 180.54N.
BASICS
HOW TO GET THE COMPONENT OF A
FORCE AND RESULTANT OF FORCES
Find the x and y componentsof theforce
F  800lbs with angle400 at III Quadrant.
Solution: Expresstheforceas F  800(180 40)  8002200
ENTER :
DISPLAY:
8002200
 612.8355545 5142300877
i
Answer : T he x componentis - 612.84lbsand
the y componentis - 514.23lbs.
BASICS
HOW TO GET THE COMPONENT OF A
FORCE AND RESULTANT OF FORCES
Find theresultuntof theforces,F1  350Nat 600
and F2  400Nwith an of angle1400.
Solution : T heresultantis thesum of thecomplex
numbers35060  400140
ENTER :
DISPLAY:
Answer : T hemagnitudeof the
resultantis 575.43Nwith 103.200
350600  4001400
575.4315683103.2017875 with the x - axis(counterclockwise)
BASICS
PAST EE/ECE BOARD EXAM
Simplify the expression i1997  i1999 wherei is an imaginarynumber.
T echnique: Divide theexponentsto 4 and get theremainder.
ENTER :
DISP LAY:
ENTER :
1997 4 DISP LAY:
1
499
4
1999 4
499
Not e:1/4 corresponds t o i (i1  i)
2/4 corresponds t o - 1 (i2  i)
3/4 corresponds t o - i (i3  - i)
whole number (0 remainder)
3
4
ENTER :
DISPLAY:
i i
0 (Answer)
corresponds t o1 (i4  1)
ADVANCE
PAST CE/ECE BOARD EXAM
Find thevalueof (1  i)5 wherei is an imaginarynumber?
T echnique: Rewriteas (1  i)3 (1  i)2
ENTER :
ENTER :
DISPLAY:
(1  i)3 (1  i) 2
 4  4i
ADVANCE
MODE 3 :
STATISTICAL AND
REGRESSION
CALCULATIONS
HOW TO FIND THE MEAN AND
STANDARD DEVIATION
Five light bulbs burned out afterlasting867,
859,840,852,and 888hrs. Find themean.
DISP LAY:
DISP LAY:
x
861.2
1
2
3
4
5
x
867
859
840
852
888
BASICS
PAST ME BOARD EXAM
Given thefollowingstatistical data,determine
thestandarddeviation.
Data:112 132 144 156 164 176 183 197
ENTER
DISP LAY:
x
1
112
2
3
4
132
144
156
5
6
7
164
176
183
8
197
DISPLAY:
x
26.21545346
BASICS
HOW TO GET THE MEAN, VARIANCE
AND STANDARD DEVIATION OF
GROUPED DATA
DISP LAY:
x
1
62
2
3
4
5
6
7
FREQ
2
65
68
71
5
12
15
74
77
80
8
5
3
BASICS
HOW TO GET THE MEAN, VARIANCE
AND STANDARD DEVIATION OF
GROUPED DATA
DISP LAY:
n
50
DISPLAY:
x
70.94
DISPLAY:
sx
4.391132065
DISPLAY:
Ans2
19.28204082
BASICS
HOW TO FIND AREAS IN THE
NORMAL CURVE
P(a)meansarea fromz  -  to z  a
R(a) meansarea fromz  a to z   
Q(a) meansarea fromz  0 to z  a
BASICS
HOW TO FIND AREAS IN THE
NORMAL CURVE
Find thearea under thenormalcurve to theleft
of z  1.64.
ENTER :
DISP LAY:
P (1.64)
0.9495
BASICS
HOW TO FIND AREAS IN THE
NORMAL CURVE
Find thearea beneatha standardnormalcurve
between z  0 and thepoint- 1.58.
ENTER :
DISPLAY:
Q(-1.58)
0.44295
BASICS
HOW TO FIND AREAS IN THE
NORMAL CURVE
Find theprobability thata normaldistribution random
variable will be within z  1 standarddeviationof themean.
Solution : We are lookingfor thearea fromz  -1 to z  1.
ENTER :
DISPLAY:
Q(-1) Q(1)
0.68268
BASICS
HOW TO FIND AREAS IN THE
NORMAL CURVE
Find theprobability thata normallydistributed random variable
will lie more than1.5 standarddeviationabove themean.
Solution : Weare lookingfor thearea fromz  1.5 to z  .
ENTER :
DISP LAY:
R(1.5)
0.066807
BASICS
HOW TO SOLVE LINEAR REGRESSION
PROBLEMS
BASICS
HOW TO SOLVE LINEAR REGRESSION
PROBLEMS
ENTER :
DISP LAY:
DISP LAY:
A
3.1359045
DISP LAY:
B
0.40449955
409
1
2
3
4
x
20
18
16
14
y
12
10
11
6
5
6
7
8
10
8
6
4
7
8
4
6
9
10
2
0
5
2
BASICS
HOW TO SOLVE LINEAR REGRESSION
PROBLEMS
T herefore: T heregressionequationsis Y  A  BX
Y  3.1359045 0.40449954
09X
b. To determine the correlatio n coefficien t :
DISPLAY:
r
0.8854825905
c. T o predict the valueof Y when X  23:
DISPLAY:
23y
12.43939394
BASICS
HOW TO GET THE EQUATION OF A
LINE GIVEN 2 POINTS
PAST ECE BOARD EXAM
Find theequationof theline thatpasses through
(2,5)and (-3,8).
DISPLAY:
ENTER :
1
2
DISPLAY:
A
31 5
x
y
2
3
5
8
DISP LAY:
B
3
5
BASICS
HOW TO GET THE EQUATION OF A
LINE GIVEN 2 POINTS
PAST ECE BOARD EXAM
T herefore: theequat ionof theline is : Y  A  BX
31 3
Y  X
5 5
or :
5Y  31 3 X
3 X  5Y  31
BASICS
HOW TO GET A POINT ON THE LINE
GIVEN TWO POINTS
If a line passes through(4,1)and (3,-7)and (x, y)
is on theline,what is the value of x in (x,4)and
the value of y in (-5,y)?
DISP LAY:
4 xˆ
Answer : When x  4, y 
35
8
35 8
BASICS
HOW TO GET A POINT ON THE LINE
GIVEN TWO POINTS
DISP LAY: Answer : Wheny  - 5, x  - 71
 5 yˆ
 71
BASICS
PAST ME BOARD EXAM
T heequationof theline thatinterceptsthe x - axis at x  4 and
the y - axis at y  - 6 is :
ENTER :
DISP LAY:
ENTER :
x y
1 4 0
2 0 6
DISP LAY:
A
-6
ENTER :
DISP LAY:
Answer :
B
1.5 or 3/2
Y  A  BX
Y  - 6  3/2X
which can be rewrit t enas :
3X - 2Y - 12  0
ADVANCE
PAST CE/ECE BOARD EXAM
Find the30th termof thearithmeticprogression 4, 7,10...
ENTER :
DISPLAY:
x
y
1 1 4
2 2 7
ENTER :
DISPLAY:
30 Ŷ
91
ADVANCE
PAST CE/ECE BOARD EXAM
Whatis thesum of theprogression 4, 9,14...up to the20th term?
ENTER :
DISPLAY:
ENTER :
x
y
DISPLAY:
1 1 4
2 2 9
A
DISPLAY:
1
Ans  A
1
ENTER :
DISPLAY:
ENTER :
ENTER :
B
DISP LAY:
5
Ans  B
5
ADVANCE
PAST CE/ECE BOARD EXAM
Whatis thesum of theprogression 4, 9,14...up to the20th term?
ENTER :
DISP LAY:
20
 A  BX
x 1
1030
ADVANCE
PAST CE BOARD EXAM
T he4th termof theGP is 216and the6th termis 1944.Find the8th term.
ENTER :
DISPLAY:
x
1 4
2 6
y
216
1944
ENTER :
DISPLAY:
8Ŷ
17496
ADVANCE
MODE 4 :
SPECIFIC NUMBER
SYSTEMS
CALCULATIONS
HOW TO DO BASE NUMBER
CALCULATIONS
Convert23410 to binary(base 2).
ENTER :
DISP LAY:
234
Dec
234
ENTER :
Thus: 23410  111010102
DISPLAY:
234
Bin
0000000011
101010
BASICS
HOW TO DO BASE NUMBER
CALCULATIONS
Convert123410 to HEXADECIMAL system.
ENTER :
ENTER :
DISPLAY:
1234
Hex
000004D2
Thus:123410  000004D216
BASICS
HOW TO DO BASE NUMBER
CALCULATIONS
ConvertABC1216 toOCTALsystem.
ENTER :
ENTER :
DISP LAY:
ABC12
Oct
0000253602
2
Thus: ABC1216  00002536022
8
BASICS
HOW TO DO BASE NUMBER
CALCULATIONS
Evaluate(AB16 )(3F16 ).
ENTER :
ENTER :
DISPLAY:
AB x 3F
Hex
00002A15
BASICS
HOW TO DO BASE NUMBER
CALCULATIONS
Evaluate112  4510  AB216  778. (in base 10)
Solution : Convert all values to base 10.
For 112
Result : 3
For AB216
Result : 2738
For 778
Result : 63
Add : 3  45  2738 63
Answer : 2849
BASICS
HOW TO DO BASE NUMBER
CALCULATIONS
Find thelogical AND ( 1012 and1102 )
ENTER :
DISP LAY:
101and110
Bin
0000000000
000100
BASICS
HOW TO DO BASE NUMBER
CALCULATIONS
Find thelogical XOR ( 1012 and1102 )
ENTER :
DISP LAY:
101xor11
Bin
0000000000
000110
BASICS
MODE 5 :
EQUATION
SOLUTION
HOW TO SOLVE EQUATIONS
IN 2 UNKNOWNS
SOLVE 2 x  7 y  4
x  2y 1
BASICS
PAST ME BOARD EXAM
In 5 years, Ana' s agewill betwice as the ageof
her friend Jun. Five years ago, she was three
tim esas old as his friend. Find their presentages.
BASICS
PAST ME BOARD EXAM
BASICS
PAST EE BOARD EXAM
A man has 2 investments one paying3% annualinterest
and theotherat 4% interest.T he totalincomefrom
theinvestments is P1700.If theinterestrates were
interchanged, the totalincomewould be P1800.
Find theamountof each investment.
BASICS
PAST EE BOARD EXAM
BASICS
PAST ECE BOARD EXAM
2000kg of st eelcont aining8% nickelis t o be
made by mixingst eelcont aining14% nickel wit h
anot hercont aining6% nickel.How much of each
is needed?
Solution:
Let : X  amountof steelcontaining14% nickel
Y  amountof steelcontaining6% nickel
BASICS
PAST ECE BOARD EXAM
BASICS
HOW TO SOLVE
QUADRATIC EQUATIONS
Solve thequadraticequation6x  7 x  5  0
2
BASICS
HOW TO SOLVE
QUADRATIC EQUATIONS
Find the values of xin x2  2x  5  0
BASICS
HOW TO SOLVE
QUADRATIC EQUATIONS
Solve thequadraticequation5x 2  2x  9  0
NOT E: T hisis theadvantageof CASIO ES PLUS
over theOLD ES - It can give irrationalroots
BASICS
HOW TO SOLVE EQUATIONS
IN 3 UNKNOWNS
Find the values of x, y and zif:
3x - 3 y - z  4
x  9 y  2 z  16
x - y  6 z  14
BASICS
HOW TO SOLVE EQUATIONS
IN 3 UNKNOWNS
BASICS
HOW TO SOLVE CUBIC
EQUATIONS
Solve thecubic equation x3  2x 2 -5x - 6  0
BASICS
HOW TO SOLVE CUBIC
EQUATIONS
Solve x - 1  0
3
BASICS
MODE 6 :
MATRIX
CALCULATIONS
HOW TO SOLVE PROBLEMS
INVOLVING MATRICES
PAST ECE BOARD EXAM
 3 5  9 1 
Simplify 37 1  2 7 1
4 9 8 9
 3 5
Solution : Store 7 1 to MAT A
4 9
ENTER :
9 1 
Solution : Store 7 1 to MAT B
8 9
ENTER :
BASICS
HOW TO SOLVE PROBLEMS
INVOLVING MATRICES
PAST ECE BOARD EXAM
ENTER :
DISP LAY:
3 MAT A  2 MAT B
ENTER :
DISP LAY:
Ans
 27 17
 35 5 


 28 45
BASICS
HOW TO SOLVE PROBLEMS
INVOLVING MATRICES
 3 2 - 1
Find the transposeof mat rixA if A   3 7 8 
- 1 3 2 
 3 2 - 1
St ore  3 7 8  t o mat rixA.
- 1 3 2 
ENTER :
ENTER :
DISP LAY: T rn (Mat A) Ent er:
Ans
 3 3 - 1
2 7 3


- 1 8 2 
BASICS
HOW TO SOLVE PROBLEMS
INVOLVING MATRICES
 2 1 3
Find t heinverseof mat rixA if A  6 1 4
3 7 2
2 1
St ore 6 1
3 7
3
4 t o mat rixA.
2
ENTER :
ENTER :
DISP LAY: Mat A-1
Ans
- 0.4 0.2923 0.0153
 0

0.076
0.1538


 0.6 - 0.169 - 0.061
BASICS
HOW TO COMPUTE THE
DETERMINANT OF A 3X3 MATRIX
Find thedeterminant :
2 4 -5
2 1 7
8 1 2
ENTER :
DISP LAY:
det(Mat A)
228
BASICS
PAST CE BOARD EXAM
In a Cartesiancoordinates, the verticesof a triangleare defined by
thefollowingpoints(-2,0),(4,0)and (3,3).Whatis thearea?
Concept: T hearea of any t riang
le wit h vertices (x1 , y1 ), (x 2 , y 2 ) and (x3 , y 3 ) is :
x1
A
1
x2
2
x3
y1
2 0 1
1
y2 1
y3 1
A
1
det 4
2
3
0 1
3 1
ENTER :
DISP LAY:
ENTER :
-2 0 1
4 0 1
3 3 1 DISP LAY:
0.5det (MatA)
9
ADVANCE
MODE 7 :
GENERATING TABLE
FROM A FUNCTION
HOW TO TABULATE VALUES OF A
FUNCTION
T abulatevaluesof f(x)  x 3  2x2  3 from
x  0 to x  10 everyunit step.
ENTER :
DISP LAY:
1
X
0
2
1
0
3
4
2
3
13
42
5
4
93
6
7
5
6
172
285
8
7
438
9
10
8
9
637
888
11
10
1197
F(X)
3
BASICS
MODE 8 :
VECTOR
CALCULATIONS
HOW TO DO VECTOR CALCULATIONS
Given the2 vectors: A  4i - j  7k and B  3i  5j  9k.
a. Find themagnitudeof theresultantof vectorsA and B.
b. Find thedot product of vectorA and B.
c. Find thecross product of vectorsA and B.
ENTER :
DISP LAY:
A
[
4
-1
7 ]
ENTER :
DISP LAY:
B
[
3
5
9 ]
BASICS
HOW TO DO VECTOR CALCULATIONS
ENTER :
DISPLAY:
Abs(VctA VctB)
17.9164728
7
b. ENTER :
DISP LAY:
Vct A  Vct B
70
c. ENTER :
DISPLAY:
VctA  VctB
Ans
[ - 44
- 15
23]
BASICS
HOW TO DO VECTOR CALCULATIONS
PAST ME/CE BOARD EXAM
Whatis themagnitudeof the vectorA  4i  2j  7k
and give its directioncosine vector.
ENTER :
ENTER :
T o get themagnitude:
ENTER :
BASICS
HOW TO DO VECTOR CALCULATIONS
PAST ME/CE BOARD EXAM
DISP LAY:
Abs (Vct A)
8.30662386
3
Not e: (T hisis storedin Ans)
T o get thedirectioncosine:
DISPLAY:
Ans
[0.4815 0.2407 0.8427]
BASICS
THANK YOU VERY
MUCH AND
GOD BLESS!!!