Unit 4 - Assignment 2 v1 Trig Methods & Standard

```BTEC Assignment Cover Sheet
BTEC Course
Level 3 Diploma in Engineering
BTEC Unit
4 – Mathematics for engineering technicians
Assignment Title
Trigonometric Methods and Standard Formulae
Teacher(s)
C Woodhouse
Issue Date
Signature of Teacher
Date
Learners Authentication of Their Work
Learners Name
Signature of Learner
Date
Internal Verification
Date
12/12/2013
P4
P5
P6
P7
Signature of Internal Verifier
BTEC Level 3 Diploma in Engineering
Unit 4 – Mathematics for engineering technicians (10 Credits)
Assignment Title - Trigonometric Methods and Standard Formulae
Introduction
As part of your engineering training programme it is a requirement that your mathematical
ability is tested. This assignment will look at your ability to use trigonometric methods and
standard formulae to determine areas (LO 2).
1)
A sector of a circle has radius 6cm and an angle of 100&deg; at its centre.
i)
Calculate the arc length.
ii)
Calculate the total perimeter of the sector.
ii)
Calculate the sector area.
2)
Change the following angles from degrees to radians,
either writing the answer as a fraction of π, or giving correct to 3 decimal places
i)
30&deg;
ii)
270&deg;
iii)
70&deg;
3)
Change the following angles from radians to degrees,
giving the answer correct to 1 dp where needed
π
3π
i)
/2
ii)
/8
iii)
4)
Work out the value of length 𝒙 and angle ϑ in the diagrams below:
i)
ii)
iii)
𝒙
𝒙
14m
0
27
0
40
3.8cm
5)
Make sketches of the following trigonometric graphs
i)
𝒚 = sin ϑ, for 00≤ ϑ ≤ 3600
𝝑
11m
9.5m
ii)
𝒚 = cos ϑ, for -1800≤ ϑ ≤ 1800
iii)
𝒚 = tan ϑ, for 00≤ ϑ ≤ 3600
6)
A
A triangular strut ABC has a tension of 14N along AB.
The angle BAC = 25&deg; and the angle ACB is 75&deg;.
What is the magnitude of the force on the strut BC?
14N
760
480
B
7)
Three forces of 15N, 20N and FN are in equilibrium, as shown in the diagram.
The angle between the 2 known forces is 1280.
Calculate the magnitude of force F.
15N
1280
FN
20N
C
8i)
8ii)
Work out the volume and the total surface area
of this cylinder,
with diameter 18cm and height 15cm
A toy is made up from a cone and a hemisphere.
The base radius of the cone is 6cm
and it has a vertical height of 8cm.
Work out the volume of the toy,
and the total surface area.
18cm
15cm
```