Transforming trigonometric graphs in engineering
A collection of resources to provide ideas for setting the transformation of trigonometric graphs in the context of engineering, together with materials to support the teaching of this topic.
'Tunnelworks: Key Stage Five Mathematics' uses transformations of trigonometric graphs to develop a simplified tidal chart for London Bridge. This understanding is then applied to modify a chart for the Thames Tideway Tunnel construction site.
There are two supporting resources. 'Exploring Trigonometrical Graphs A12' is a resource from the DfE Standards Unit. Students explore trigonometrical graphs by recognising translations, stretches, and reflections from their equations. 'Trigonometrical Functions' is a 'Further Thinking Questions resource, from Susan Wall. It contains twelve problems exploring the properties of trigonometrical functions, including properties of their graphs.
Tunnelworks: Key Stage Five Mathematics
In using this resource, students generate and transform trigonometric graphs. They use translations and stretches to develop a simplified tidal chart for London Bridge before applying their understanding to modify their chart for a Thames Tideway Tunnel construction site that will be built in the foreshore of the River Thames.
Exploring Trigonometrical Graphs A12
In this resource from the DfE Standards Unit, students explore trigonometrical graphs by recognising translations, stretches and reflections from their equations, sketching the graphs and learning about the period and amplitude. Students should be familiar with the graphs of y = sin x and y = cos x and have previously met the basic transformations of functions, i.e. one-way stretches, translations and reflections, but not necessarily in the context of trigonometrical graphs (AS / A2 level). This work would be helpful to use ahead of students working on the 'Tunnelworks: Key Stage Five Mathematics' resource.
Trigonometrical Functions
This Further Thinking Questions resource, from Susan Wall, contains twelve problems requiring students to explore the properties of the functions of sine, cosine and tangent. The problems are designed to encourage rich discussion in the classroom, by asking students to explain which is the odd one out, match functions with their graph, devise questions which give a certain set of solutions or state whether statements are true sometimes, always or never. The resource would make an ideal complement to the engineering resource 'Tunnelworks: Key Stage Five Mathematics'.