Introducing Trigonometry
Activity
The Aim and The Description

Constructing triangles

Tags - GCSE, HS, SSM, Introducing Trigonometry, investigation

Aim - for students to investigate and discover the patterns for a ratio in similar triangles and thus understand the basic premis behind the meaning of 'Sine 30'

Description - In This activity students are aked to construct triangles with pencil, ruler and compass given specific instructions 'they should all be similar). They are asked to measure the remaining features of the triangles and comment on the similarities. Students then calculate the sine ratio for the angle (which should be 30°) and make a statement about what this means for this set of similar triangles. Students are then asked to verify their results using Cabri

Activity - Printable
Why? What? How?

Investigating the Sine ratio

Tags - GCSE, HS, SSM, Introducing Trigonometry, investigation, IT

Aim - In the first instance, for students to demonstrate for themselves that the ratio of opposite to hypotenuse for all 30, 60, 90 triangles remains 0.5 . Students then use the Cabri Calculator to investigate the sine ratio for other angles between 0 and 90. There is potential for intersteing discsussion about both of these limits.

Description - The Cabri calculator has been pre designed for students us. First students use it verify that sin 30 = 0.5 by enlarging the triangle in the file, measuring the relevant sides and calculating the ratio. Students then change the angle and conclude about the sin of other angles; their results are collected and in table and plotted on a graph. the graph is then used to make predictions and begin the notion of solving problems before using the calcultor to work it out.

Activity - Printable
Cabri calculator
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Making and using a Cabri Calculator for Sin, Cos and Tan

Tags - GCSE, HS, SSM, Introducing Trigonometry, create, IT, investigation

Aim - For students to extend their understanding of the geometric origins of sin, cos and tan by constructing the triangles that can be used to calculate the ratios

Description - Students are shown the cabri-calculator for sin (degree of explanation offered by the teacher depends on the class and their fluency with the program) and asked to construct their own for cos and tan. (Of course, these three can all be done on the same file). students are then asked to use the calculators to investigate some patterns. For example, that for 0 to 90 cos is a reflection of sin and sin 30 = cos 60.

Activity - Printable
Cabri - Calculator + instructions
Why? What? How?

Making Statements

Tags - GCSE, HS, SSM, Introducing Trigonometry, worksheet

Aim - For students to become familiar with the idea of analysing triangles with trigonometrical statements before using trigonometry to solve problems.

Description - Students are given a diagram containing right angled triangles. The angles and dimensions are all given algebraic symbols. Students are asked to make as many correct statements about the diagram as possible. Some students may extend this to the use of pythagoras' theorem and calculations of area.

Activity Printable
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Solving trig Equations

Tags - GCSE, HS, SSM, Introducing Trigonometry, investigation

Aim - For students to recap the simple relationship between 3 variables that allows each of them to be made the subject and to then use this to solve trig equations.

Description - This worksheet asks students to recall simple incerse operations to change the subject of a simple 3 variable formula and gradually leads on to applying this to sipmle trig equations and thus on to solving simple right - angled trig problems

Activity Printable
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Practise

Tags - GCSE, HS, SSM, Introducing Trigonometry, investigation

Aim - For students to practise solving trig problems and extend themselves using these principles

Description - This is a worksheet of right-angled trig problems that extends to word and more complex problems

Activity Printable
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