Download Unit_4_ASSIGNMENT 2

BTEC NATIONAL EXT DIPLOMA IN ENGINEERING
500/8165/2
UNIT 4 – MATHEMATICS FOR ENGINEERING TECHNICIANS (A/600/0253)
ASSIGNMENT TWO - Trigonometric Methods and Standard Formulae
LEARNER NAME
ASSESSOR NAME
F. NDORO
DATE ISSUED
HAND IN DATE
SUBMITTED ON
Criteria
Task
P4 solve circular and triangular measurement problems
involving the use of radian, sine, cosine and tangent
functions
Task 1
Achieved
Feedback
Task 2
HEALTH AND SAFETY LEGISLATION,
REGULATIONS AND
Task PRACTICES
3
P5 sketch each of the three SAFE
trigonometricWORKING
functions over
IN FABRICATION
a complete cycle
P6 produce answers to two practical engineering
problems involving the sine and cosine rule
Task 4
P7 use standard formulae to find surface areas and
volumes of regular solids for three different examples
respectively
Task 5
This brief has been verified as fit for purpose
Internal Verifier
ANTHONY SPICER
Signature
A J Spicer
Date
1
Our Lady & St John Catholic College Engineering
27/07/2012
BTEC NATIONAL EXT DIPLOMA IN ENGINEERING
500/8165/2
Assessor's comments
Qualification
Edexcel Lev 3 National Diploma in
Engineering
Assessor name
Unit number and title
Unit 4 – Mathematics for Engineering
Technicians (A/600/0253)
Learner name
F. NDORO
Assignment title
ASSIGNMENT TWO – Trigonometric Methods and Standard Formulae
Grading criteria
Achieved?
P4 solve circular and triangular measurement problems involving the use of radian, sine, cosine and tangent functions
P5 sketch each of the three trigonometric functions over a complete cycle
P6 produce answers to two practical engineering problems involving the sine and cosine rule
P7 use standard formulae to find surface areas and volumes of regular solids for three different examples respectively
Learner feedback
Assessor feedback
Action plan
Assessor signature
Date
Learner signature
Date
2
Our Lady & St John Catholic College Engineering
BTEC NATIONAL EXT DIPLOMA IN ENGINEERING
500/8165/2
TASK 1 - CIRCULAR MEASURE CALCULATIONS
P4 solve circular and triangular measurement problems involving the use of radian, sine, cosine and
tangent functions
1.(a) Convert 720 from degrees to
(i) radians (ii) revolutions
(b) Convert

radians to
2
(i) degrees
(ii) revolutions
(c) Convert 6 revolutions
(i) degrees
(ii) radians
[P4 Part]
Leave your answers as multiples of pi   for revolutions and
radians in all cases above
2. Work out the length of each arc and area of each sector to 2 decimal
places using the following formulas for area of sector and length of an
arc:
Where r is the radius of the circle and  is the angle subtended at the
centre in radians.
(a) Radius = 10cm, angle subtended at centre = 720
(b) Radius = 100cm, angle subtended at centre =   /2 rad
[P4 Part ]
3
Our Lady & St John Catholic College Engineering
BTEC NATIONAL EXT DIPLOMA IN ENGINEERING
500/8165/2
TASK 2 - TRIANGULAR MEASURE – SINE, COSINE & TANGENT RULE
P4 solve circular and triangular measurement problems involving the use of radian, sine, cosine and
tangent functions
1. A 5m ladder leans against a
wall as shown on the left.
(a) Use the tangent rule to find
the angle between the ladder
and the wall?
(b) Use the sine function to find
the angle between the ladder
and the floor
(c) Use the cosine function to
check if the answer obtained in
(a) is correct
2. Three forces acting on a fixed point are represented by three sides of a
triangle ABC of dimensions 7.0 cm, 12.6 cm and 18.25 cm. Determine the
angles between the directions of the three forces. (Apply the cosine and sine
rules)
[P4 Part]
4
Our Lady & St John Catholic College Engineering
BTEC NATIONAL EXT DIPLOMA IN ENGINEERING
500/8165/2
TASK 3 – GRAPHS OF SINE, COSINE AND TANGENT OVER A FULL
CYCLE
P5 sketch each of the three trigonometric functions over a complete cycle
TASK 1
(a) Using the same axis, plot the graphs of
1:
2:
3:
Over the range   0 0 to720 0
(b) comment on the periodic cycles of the drawn curves above
[P5]
5
Our Lady & St John Catholic College Engineering
BTEC NATIONAL EXT DIPLOMA IN ENGINEERING
500/8165/2
TASK 4 – APPLICATION OF SINE AND COSINE RULE IN ENGINEERING
P6 produce answers to two practical engineering problems involving the sine and cosine rule
Fig 1 below shows a wall crane.
1. Find the length of the tie and the angle the tie makes with the wall.
Fig. 1
2. The drawing below shows a metal piece after it has been cut out using the
blanking process; dimensions for all sides are in mm.
i) Find the length AC
ii) Find the angle ADC
[P6]
6
Our Lady & St John Catholic College Engineering
BTEC NATIONAL EXT DIPLOMA IN ENGINEERING
500/8165/2
TASK 5 – STANDARD FORMULAE FOR SURFACE AREAS AND
VOLUMES OF REGULAR SOLIDS
P7 use standard formulae to find surface areas and volumes of regular solids for three different
examples respectively
1. Use standard formulae to find surface areas and volumes of the prisms
below.
Surface Area
Volume
Surface Area
Volume
Surface Area
Volume
7
Our Lady & St John Catholic College Engineering
BTEC NATIONAL EXT DIPLOMA IN ENGINEERING
500/8165/2
Student declaration
I declare that all the work submitted for this assignment is my own work or, in the case of group
work, the work of myself and the other members of the group in which I worked, and that no
part of it has been copied from any source.
I understand that if any part of the work submitted for this assignment is found to be plagiarised,
none of the work submitted will be allowed to count towards the assessment of the assignment
Signed …………………………………… Date ………………………………
8
Our Lady & St John Catholic College Engineering
BTEC NATIONAL EXT DIPLOMA IN ENGINEERING
Our Lady & St John Catholic College Engineering
500/8165/2
9