MathsMate: Physics P&A
These modules are selected from the MathsStart and MathsTrack bridging programs (see link below). They cover the knowledge assumed in Physics: Principles and Applications for
- Trigonometry
- Differentiation
Use the menu bar at the end of the page to return or to contact the Maths learning Service.
This module introduces trigonometric ratios and their properties.
Trigonometry was developed by the ancient Greeks and Hindus to find distances that were not easily accessible, for example the mathematician Eratosthenes used it to calculate the radius of the earth in the third century BCE. Today, it is used extensively in engineering, surveying, architecture and astronomy. It is also used in many other mathematical applications.
Contents- 1. Right-angled Triangles and Trigonometric Ratios.
- 2. Sine, Cosine and Tangent
- 3. Properties
Prerequisites
- scientific calculator
This module introduces a new way of thinking about angles, and extends the definitions of sine, cosine and tangent to angles greater than 90°. It explores the properties and graphs of the trigonometric functions sin θ, cos θ and tan θ, and their applications.
Contents
- 1. Measuring Angles
- 2. Sine, Cosine and Tangent Functions
- 3. Applications
- 4. Identities (optional)
- 5. Radian Measure (optional)
Prerequisites
- scientific calculator
- trigonometric ratios
This module introduces the gradient of a curve. This concept was invented by Pierre Fermat in the 1630s and made rigorous by Issac Newton and Gottfried Leibniz in the 1670s.
The process of finding the gradient by algebra is called differentiation. It is a powerful mathematical technique and many scientific discoveries of the past three centuries would have been impossible without it. Newton used these ideas to discover the Law of Gravity and to find equations describing the orbits of the planets around the sun. Differentiation remains a powerful technique today and has many theoretical and practical applications.
Contents
- 1. Describing Change
- 2. Differentiation
- Appendix A: The gradient of a straight line
- Appendix B: Polynomials
Prerequisites
- Appendix A.