EN0018: Introduction to Trigonometry

School Cardiff School of Engineering
Department Code ENGIN
Module Code EN0018
External Subject Code 100403
Number of Credits 10
Level L3
Language of Delivery English
Module Leader DR Alistair Reid
Semester Autumn Semester
Academic Year 2025/6

Outline Description of Module

This module provides a comprehensive foundation in trigonometric concepts and techniques that are essential for solving a wide range of engineering problems. Aimed at students new to tertiary-level engineering the module covers key topics such as radians, degrees, trigonometric ratios, solving triangles, sine and cosine rules, trigonometric graphs, identities, inverse functions, and complex numbers. The syllabus is structured to build both theoretical understanding and practical problem-solving abilities, with weekly topics reinforced through lectures, tutorials, and interactive exercises. Students will develop a robust toolkit for addressing multidimensional engineering challenges laying a solid mathematical foundation for advanced studies and professional practice in engineering. 

On completion of the module a student should be able to

  • LO1. Use radians, degrees, Pythagoras’ Theorem and similar triangles to perform conversions and solve a range of problems. 
  • LO2. Critically analyse a range of engineering and geometric problems through application of trig ratios, the sine rule, the cosine rule and ‘special triangles’. 
  • LO3. Exercise critical judgement in applying inverse trig functions and trig identities demonstrating understanding of their application to solving and modeling engineering problems. 
  • LO4. Analyse and model periodic phenomena, recognising, plotting and interpreting their graphs and solve and range of problems using imaginary and complex numbers. 
  • LO5. Plan self-learning and communicate effectively in discussing solutions to exercises with peers. 

 

 

 

How the module will be delivered

The module will be delivered through a blend of online teaching and learning material, guided study, and on-campus face-to-face classes (tutorials, feedback sessions). Extensive notes for pre/post lecture reading will be provided together with suggested further reading.

Skills that will be practised and developed

Subject-Specific Skills 

  • Exercising critical judgment in solving a variety of mathematical problems within the domain of trigonometry, ranging from degrees, radians, Pythagoras, trig ratios, sine and cosine laws, trig identities, surds, invers trig functions, modelling and interpreting periodic functions, phase shift, period, imaginary numbers and complex numbers and their cartesian and polar forms. 

  • Application of appropriate trigonometric techniques to solve engineering problems. 

  • Planning, self-learning and communication through a range of interactive sessions, tutorials and exercises. 

 

Transferable/Employability Skills (Graduate Attributes): 

  • Independent and critical thinkers 

    • ICT1: Identify, define and analyse complex issues and ideas, exercising critical judgement in evaluating sources of information 
    • ICT2: Demonstrate intellectual curiosity and engage in the pursuit of new knowledge and understanding 
    • ICT3: Investigate problems and offer effective solutions, reflecting on and learning from successes and failures 
  • Reflective & Resilient 

    • RR1: Actively reflect on own studies, achievements and self-identity 
    • RR2: Demonstrate resilience, adaptability and creativity in dealing with challenges, and be open to change 
    • RR3: Identify and articulate own skills, knowledge and understanding confidently and in a variety of contexts 
    • RR4: Engage with new ideas, opportunities and technologies, building knowledge and experience to make informed decisions about own future 

How the module will be assessed

SUMMATIVE ASSSSMENT  

This module is assessed through an in-class test and an exam: 

  • The test will cover module syllabus up to week 6 and will occur mid-semester. This component worth 20% of the overall module mark (LO 1,2,5). 

  • The exam will coverall all module syllabus covered over the course of the semester and will take place in the January exam period. This component worth 80% of the overall module mark (LO 1,2,3,4,5). 

FORMATIVE ASSESSMENT  

Students will have access to support and feedback through interactive sessions and exercises.  

THE OPPORTUNITY FOR REASSESSMENT IN THIS MODULE: 

There is a potential for re-assessment in this module which may result in a 100% assessment during the August Resit period prior to the start of the following academic session. 

Opportunities for re-assessment is only permitted provided you have not failed more credit than in the resit rule adopted by your programme.  If the amount of credit you have failed is more than permitted by the relevant resit rule, you may be permitted to repeat study if you are within the threshold set for the Repeat rule adopted by your programme.  You will be notified of your eligibility to resit/repeat any modules after the Examining Board in the Summer period. 

Assessment Breakdown

Type % Title Duration(hrs)
Class Test 20 In-Class Test N/A
Class Test 80 Exam N/A

Syllabus content

  • Use of radians and degrees 

  • Similar triangles and trig ratios 

  • Pythagoras’ theorem and special triangles 

  • Solving triangles 

  • Sine and cosine rules 

  • Trig graphs 

  • Trig identities and formulae 

  • Inverse trig functions 

  • Modelling with trig functions 

  • Complex numbers 


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