(contributor: Anna Cox)
How do I use trigonometry as a tool to teach algebra?
To introduce trigonometry, I lead the students from numerical measurements and calculations into forming algebraic representations and using algebra to find unknowns. In this case, trigonometry formed a context from which I could teach and reteach algebraic processes and concepts.
We started with giant cardboard triangles. All of the students had different right angled triangles, with different side and angle sizes to work with. I modelled the steps on the white board as I asked every student to measure and record the length of the sides of her triangle. Each student was then asked to cut her triangle to form a similar triangle. I instructed students to repeat our measurements. Students found that the ratios of two similar sides were always the same (within limits of the accuracy of our instruments)…so from this conjecture, we renamed our ratios as sine, cosine and tangent of the angle of our triangles. We then set about using these trig ratios (and the knowledge that our calculators stored all these marvellous measured ratios for all the possible angles we could imagine) to solve problems.
Below are the scanned pages from studentR’s workbook showing her earliest exercises in trigonometry. The pages shown are from two consecutive days’ work. Notice that from the start, studentR is directed towards using good habits for setting out her work. Notice that on the second day, she is forming her own approach and I realised I needed to help her use standard conventions. I am pleased see that she is listing what she knows, but I am not happy about the use of a division sign instead of fraction notation. This shows me that she is tending to think across the page instead of working down through lines of reasoning.
 Anna explains why she developed this resource

Trigonometry Tools studentR work sample day 1
4.012 Trigonometry Tools studentR work sample 1

Trigonometry Tools studentR work sample day 2
4.012 Trigonometry Tools studentR work sample 2
As my students progressed through the topic, I gave them mixtures of right angle triangle problems to solve. I encouraged my students to identify the best approach for each task rather than give them sets of similar exercises or drills.
Please note that by the end of the unit of work, studentR was solving problems independently, with clearly set out working!

From the Algebra Programme Overview, Level 5 Right Angle Triangles
Level 5 Right Angle Triangles from Anna Nov 2010

Teacher notes and student work sample
4.012 Trigonometry Tools teacher notes and student work sample