| CODE | ENR0012 | ||||||||||||
| TITLE | Trigonometry and Vectors | ||||||||||||
| UM LEVEL | 00 - Mod Pre-Tert, Foundation, Proficiency & DegreePlus | ||||||||||||
| ECTS CREDITS | 6 | ||||||||||||
| DEPARTMENT | Faculty of Engineering | ||||||||||||
| DESCRIPTION | This study-unit starts with a review of trigonometric ratios and covers trigonometric and hyperbolic functions, trigonometric identities and equations and their applications. It then presents vectors and complex numbers, both of which are also important foundations for engineering. Study-Unit Aims: This study-unit aims to provide an understanding of trigonometric and hyperbolic functions and related identities, It also presents vectors in two and three dimensions and their applications and introduces complex numbers. Learning Outcomes: 1. Knowledge & Understanding: By the end of the study-unit the student will be able to: a. describe trigonometric functions, inverse trigonometric functions and hyperbolic functions; b. express angles in either degrees or radians; c. recall values of trigonometric functions of angular values π/k, where k=1, 2, 3, 4, 6, in surd or rational form; d. sketch graphs of trigonometric and hyperbolic functions, and identify the domain for the existence of inverse functions; e. recognise expressions that can be simplified using trigonometric identities; f. describe the notation of vectors in two and three dimensions; g. identify different representations for line equations; h. calculate the angle between two lines or vectors; i. understand how to compute a vector product; j. use vectors for the geometry of lines and planes; k. describe the use of vectors in mechanical and electrical engineering problems; l. describe the concept of a complex number, its basic properties and representation on an Argand diagram; m. describe De Moivre's Theorem for any rational index; n. sketch the loci of complex numbers. 2. Skills: By the end of the study-unit the student will be able to: a. determine the arc length, area of a sector and the area of a segment; b. apply trigonometric identities including fundamental identities, Pythagorean identities, compound angle identities, double and half angle identities and factor formulae; c. solve simple trigonometric equations and equations of the form: a cos θ + b sin θ = c; d. apply trigonometric approximations for small angles; e add/subtract vectors and work out the scalar and vector product of two vectors; f. construct the vector, cartesian and parametric equations of lines; g. write the equation of a plane in vector and cartesian form; h. use vector manipulations to find areas and volumes of simple shapes; i. find the angle between two planes, a line and a plane and their intersection; j. derive the polar and exponential forms of a complex number; k. use De Moivre’s Theorem to find the complex roots of a complex number and to derive trigonometric identities; l. solve equations and inequalities involving the modulus of complex numbers and sketch the corresponding loci and regions on an Argand diagram. Main Text/s and any supplementary readings: Main Texts: - Bostock, L., & Chandler, S. (1981). Mathematics : The core course for A-level. Thornes. - Bostock, L., Chandler, S., & Rourke, C. (1982). Further pure mathematics. Thornes. |
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| STUDY-UNIT TYPE | Lecture, Independent Study & Tutorial | ||||||||||||
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| LECTURER/S | Anthea Agius Anastasi Nathaniel Barbara |
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The University makes every effort to ensure that the published Courses Plans, Programmes of Study and Study-Unit information are complete and up-to-date at the time of publication. The University reserves the right to make changes in case errors are detected after publication.
The availability of optional units may be subject to timetabling constraints. Units not attracting a sufficient number of registrations may be withdrawn without notice. It should be noted that all the information in the description above applies to study-units available during the academic year 2024/5. It may be subject to change in subsequent years. |
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