Chapter 1 – Unit Circle and Definitions

Activities – Chapter 1

Note to Students:

Students should be aware that these worksheets are not ‘fill in the blank’ worksheets. We have intentionally given you no space to write answers on the worksheets. You should have a notebook for your work, perhaps even beginning by sketching ideas on a white board or scratch paper until you have sufficient organization to put a coherent explanation in your notebook. Note also that the expectation is to write ‘explanations’ and not ‘answers’. These activities are not designed to teach computational skills, but instead are designed to introduce mathematical concepts. The process used to solve problems is the focus, not the end result.

Activity 1a – Special Triangles

This first activity on the 45°- 45°- 90° triangle and the 30°- 60°- 90° triangle is designed to develop the building blocks to complete the Unit Circle in Topic 1.4. The Unit Circle is introduced in Topic 1.2 and this material in important to build upon the definitions given in Topic 1.2 to develop the complete Unit Circle in Topic 1.4. It can be done immediately prior to Topic 1.4, or can be done earlier in Unit 1, it relies only on some ideas from geometry.

Within the activity are instances where you will want to be familiar with simplifying square roots (or as it is sometimes called, simplifying ‘radicals’). You may wish to remind yourself of these simplification rules prior to this activity.

Special Triangles

Activity 1b – Piston Motion

This activity only requires knowledge of the unit circle (Topic 1.4) and therefore can be done in Unit 1, although it requires a fair amount of mathematical sophistication. This activity will help build problem-solving skills, and asks a deep question that will require a fair amount of time. It is a stand-alone activity, and could be done just about anytime during a Trig course. Ideas from Topic 1.4 are important, as well as the Pythagorean Theorem.

It is best to see the piston motion in action, and the worksheet provides a link to with an animation.

Piston Motion


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Trigonometry Copyright © 2022 by Mike Weimerskirch and the University of Minnesota Board of Regents is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License, except where otherwise noted.