**BTEC NATIONAL EXT DIPLOMA IN ENGINEERING**500/8165/2

F. NDORO

DATE ISSUED / HAND IN DATE / SUBMITTED ON

Criteria / Task / Achieved / Feedback

P4 solve circular and triangular measurement problems involving the use of radian, sine, cosine and tangent functions / Task 1

Task 2

P5 sketch each of the three trigonometric functions over a complete cycle / Task 3

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 / 27/07/2012

1

Our Lady & St JohnCatholicCollege Engineering

**BTEC NATIONAL EXT DIPLOMA IN ENGINEERING**500/8165/2

**Assessor's comments**

Qualification / Edexcel Lev 3 National Diploma in Engineering / Assessor name / F. NDORO

Unit number and title / Unit 4 – Mathematics for Engineering Technicians (A/600/0253) / Learner name

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

**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

(i) degrees (ii) revolutions

(c) Convert6 revolutions

(i) degrees (ii) radians

[P4 Part]

**Leave your answers as multiples of pi ****for revolutions and radians in all cases above**

- 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 ]

**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*

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]

**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

(b) comment on the periodic cycles of the drawn curves above

[P5]

**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]

**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.

**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 **………………………………

1

Our Lady & St JohnCatholicCollege Engineering

**BTEC NATIONAL EXT DIPLOMA IN ENGINEERING**500/8165/2

1

Our Lady & St JohnCatholicCollege Engineering