Trigonometry
This set of resources is designed to help students use trigonometric ratios, find angles and lengths in right-angled triangles in both two and three dimensional figures. Students will use exact values of sine, cosine and tangent for angle values of 00, 300, 450 and 600. Students are also required to use the alternative formula for the area of a triangle, 1/2abSinC. Students will also have the opportunity to apply the sine rule and the cosine rule.
Visit the secondary mathematics webpage to access all lists.
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- Teacher guidance
- Information sheet
- Activity sheet
Teacher guidance
Engaging Mathematics for All Learners
Engaging Mathematics for All Learners draws together the experience of teachers and their learners in a series of case studies. The rich variety of content, from using recreational activities as a starting point for classroom mathematics in a residential special school to using fashion design in a mathematics and art initiative in a selective girls' school, illustrate some of the possibilities.
Working with other subject disciplines, exploiting ICT and making sense of mathematics are some of the innovative approaches adopted by schools to enhance the learning of mathematics. In particular a number of the activities presented in the case studies include ideas for how students can apply their knowledge of trigonometry in 3 dimensions. The guide contains guidance on how to plan a compelling learning experience and some strategies for devising and working with rich mathematical activities.
Information sheet
What's the Point of... Maths
This booklet has been written to help answer one of the common questions heard in mathematics classrooms up and down the country, and even one in the Houses of Parliament - what's the point of learning all this maths stuff?
The logic and organisation of a mathematical brain helps with problem solving and each of the pages in this booklet deals with an area of mathematics showing why it is useful and what you can do with it.
The final section is on trigonometry and considers the use of trigonometry in tracking terrorists through their mobile phones and civil and military use for tracking airplanes. It then looks at a more light hearted use of trigonometry for animation in Hollywood.
Activity sheet
Trigonometry
This resource contains two packs of games, investigations, worksheets and practical activities supporting the teaching and learning of trigonometry.
Trigonometry pack two contains fourteen work cards with activities requiring students to investigate the lengths of the opposite and adjacent sides of a right-angles triangle leading to the definitions of sine and cosine, investigate an extension to Pythagoras’ theorem, use the sine and cosine ratios to solve problems, using the sine and cosine rules, explore the graphs of the sine function, use trigonometry in three dimensions, and find the angle between planes.
Related resources include answers to all of the cards and test books and answers.
Trigonometry
This activity gives students four possible properties of a triangle. Students are required to find as many triangles as they can which contain any three of these four properties. Once the triangles have been found, students are asked to find the area and perimeter of each. To complete the task students need to use the cosine rule, the sine rule and use the sine function to find the area of a triangle. This activity fits the key characteristic of a rich task as it is easy access but has a high exit point. This resource is particularly suitable for students who need practice to more able students who need to be challenged. Teacher guidance is also provided.
Circles in a Triangle
In this activity, students are presented with a series of different sized equilateral triangles each containing a number of circles, each of radius one unit. Students are required to find the exact area of each triangle.
The activity is extended into three dimensions by considering the volume of shapes packed with spheres.
As well as applying trigonometry, this rich task makes links across a number of areas and strands of mathematics including Pythagoras' theorem, surds, sequences and algebraic proof all of which are needed for success in this task. The formula for the nth term of a triangle number is needed from the start.
The resource includes a student hand out, teachers' notes and answers.
Trigonometry
This resource covers aspects of trigonometry often used in the field of engineering. They include the use of trigonometric ratios, Pythagoras’ theorem and the sine and cosine rules.
Comprehensive notes, with clear descriptions, for each resource are provided, together with relevant diagrams and examples. Students wishing to review, and consolidate, their knowledge and understanding of trigonometry will find them useful, as each topic includes a selection of questions to be completed, for which answers are provided.
