Similarity and Trigonometric Ratios

In this investigation, students will use Geogebra and Python to explore triangle similarity and trigonometric ratios.

Students begin by using enlargement transformations in Geogebra to explore properties relating to angles, side lengths, ratios between sides, and area of an enlarged triangles in comparison to the original triangle.

Next, students create a right angle triangle together with enlargements of this triangle, and investigate the ratio between sides in the triangles, leading to the introduction of the three trigonometric ratios of sine, cosine and tangent.

As an extension, students can also write, use or adapt code that calculates trigonometric ratios for sine and cosine for a given angle. Students are introduced to sine and cosine series expansions and given guidance on how to implement these expansions by writing code in Python.

This resource consists of the following files

• Trigonometry-investigation.docx task sheet for students. Can be modified to add or remove sections
• Trigonometry-investigation.pdf copy of task sheet as pdf file.
• sine_series.zip contains a Python code file for calculating trigonometric ratios using series expansions
• Setup-Instructions.docx instructions for setting up the Python code. Only required in students do step 3.