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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 Deadline 1 Final Deadline Signature of Teacher Date Learners Authentication of Their Work Learners Name Signature of Learner Date Internal Verification Final Grade Confirmed Date 12/12/2013 Grading Criteria Completed P4 P5 P6 P7 Final Grade Awarded 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). Task 1 (P4) 1) A sector of a circle has radius 6cm and an angle of 100° 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° ii) 270° iii) 70° 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) 0.7 radians 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 Task 2 (P5) 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 Task 3 (P6) 6) A A triangular strut ABC has a tension of 14N along AB. The angle BAC = 25° and the angle ACB is 75°. 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 Task 4 (P7) 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