Trigonometry - Mathematics (Undergraduate Foundation)

This course provides a complete guide to trigonometry, from the principles of circular measure to functions of any angle. It covers the unit circle definitions and culminates in a full treatment of the addition and factor formulae. This is the mathematical language of cycles, waves, and angles. A command of trigonometry is essential for any field that models periodic or geometric systems. It is used extensively in physics to analyse waves and oscillations, in engineering for structural analysis and signal processing, and in computer graphics for rotations and 3D modelling. By the end of this course, you will be able to convert between degrees and radians, define the six trigonometric functions for any angle using the unit circle, and apply the addition and factor formulae to manipulate and simplify trigonometric expressions and solve equations. This course is a mandatory prerequisite for any student of mathematics, physics, or engineering. It provides the necessary foundation for the study of calculus, complex numbers, and vector analysis.

Enrolment valid for 12 months
This course is also part of the following learning track. You may join the track to gain comprehensive knowledge across related courses.
MTH 101: Elementary Mathematics I - Algebra and Trigonometry
MTH 101: Elementary Mathematics I - Algebra and Trigonometry
Master the foundational mathematical structures essential for success in quantitative undergraduate degrees and professional technical roles. This comprehensive learning track delivers a rigorous treatment of algebra and trigonometry, moving rapidly from fundamental set theory and real number operations to advanced topics including matrix algebra, complex numbers, and analytical trigonometry. You will establish the critical problem-solving framework required for advanced study in calculus, engineering mechanics, and data science. This programme is primarily designed for first-year university students in STEM disciplines requiring strong analytical bases, particularly engineering, physics, computer science, and economics. It also serves as an intensive, high-level refresher for professionals returning to academia or shifting into data-driven roles demanding precise numerical literacy and logical structuring. Prior competence in standard secondary school mathematics is assumed; focus is placed strictly on mastery and application of core definitions. Upon completion, you will possess the skills to construct rigorous logical arguments using set theory and mathematical induction, model complex relationships with functions and matrices, and analyze periodic systems using advanced trigonometry. You will demonstrate competence in solving diverse equation types, from quadratics to linear systems, and manipulating complex numbers in engineering applications. This track prepares you directly for the mathematical demands of second-year university studies and technical professional certification exams.

Master the foundational mathematical structures essential for success in quantitative undergraduate degrees and professional technical roles. This comprehensive learning track delivers a rigorous treatment of algebra and trigonometry, moving rapidly from fundamental set theory and real number operations to advanced topics including matrix algebra, complex numbers, and analytical trigonometry. You will establish the critical problem-solving framework required for advanced study in calculus, engineering mechanics, and data science. This programme is primarily designed for first-year university students in STEM disciplines requiring strong analytical bases, particularly engineering, physics, computer science, and economics. It also serves as an intensive, high-level refresher for professionals returning to academia or shifting into data-driven roles demanding precise numerical literacy and logical structuring. Prior competence in standard secondary school mathematics is assumed; focus is placed strictly on mastery and application of core definitions. Upon completion, you will possess the skills to construct rigorous logical arguments using set theory and mathematical induction, model complex relationships with functions and matrices, and analyze periodic systems using advanced trigonometry. You will demonstrate competence in solving diverse equation types, from quadratics to linear systems, and manipulating complex numbers in engineering applications. This track prepares you directly for the mathematical demands of second-year university studies and technical professional certification exams.

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Course Chapters

1. Introduction
2
This chapter introduces the field of trigonometry. It defines its purpose as the study of relationships between the angles and side lengths of triangles and outlines its broader application to periodic phenomena, such as waves. Key objectives include understanding the course structure and the fundamental scope of trigonometry as a critical branch of mathematics for science and engineering.
Concept Overviews
2 Lessons
2. Angles and Circular Measure
2
4
This chapter covers the measurement of angles, moving from the familiar system of degrees to the fundamental mathematical concept of circular measure, or radians. Radian measure is essential for calculus and advanced trigonometry. Topics include defining radians, converting between degrees and radians, and applying radian measure to calculate the length of a circular arc and the area of a sector.
Concept Overviews
2 Lessons
Problem Walkthroughs
4 Lessons
3. Trigonometric Functions
3
4
This chapter extends trigonometry beyond right-angled triangles. It uses the unit circle to define the six trigonometric functions for any angle, a concept critical for analysing periodic phenomena. Key topics include the unit circle, defining functions for angles of any magnitude, and the graphical representation of the sine, cosine, and tangent functions.
Concept Overviews
3 Lessons
Problem Walkthroughs
4 Lessons
4. Trigonometric Identities
2
4
This chapter covers the manipulation of trigonometric expressions using standard identities. A command of these identities is essential for solving complex trigonometric equations and for simplification in calculus. Key topics covered are the addition formulae (for sin(A±B), cos(A±B)) and the factor formulae (product-to-sum and sum-to-product).
Concept Overviews
2 Lessons
Problem Walkthroughs
4 Lessons
5. Conclusion
2
This chapter consolidates the core concepts of trigonometry. It provides a structured summary of circular measure, trigonometric functions, and key identities, reinforcing the principles required for progression. The conclusion summarises the unit circle definitions and standard formulae. It also provides a forward look to how these concepts are applied in calculus and complex numbers.
Concept Overviews
2 Lessons