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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