Mathematics for Teaching Trigonometry Trigonometry – why study triangles

Trigonometry – why study triangles

Why study trigonometry?

We study Trigonometry because it is useful. Its earliest and simplest use is to find the missing part of a triangle. But mathematicians do not just study something because it is useful. More often, they study something because it is fascinating. This fascination with triangles especially in the measure of it sides and angles has developed into a coherent piece of mathematical knowledge we now call trigonometry.

Why not quadrinometry?

What is so special about triangles? Why did mathematicians created a branch of mathematics devoted to the study of it? Why not quadrinometry? Quadrilaterals, by its variety are far more interesting. Not only that, each piece of shape is related to another piece. If you know quadrilateral, you’ll know about the rest of the quadrilaterals. But this is also precisely the reason why we study trigonometry, why we study triangles. If you know it, you’ll know about any polygon not just quadrilaterals. Any polygon can be dissected into pieces of triangles! Try dissecting any of these shapes:

What’s with right triangles?

There are different kinds or shapes of triangles. In terms of angles we have equiangular, acute, obtuse, and right triangles. Why is it that we devote so much time studying about right triangles in trigonometry? Try dissecting the other triangles and you’ll know why if you know about right triangles, you’ll know about the other triangles!.












Here’s a bonus reason: when you study triangles, you don’t need to deal with nonconvex ones!
Click Teaching trigonometry through problem solving for a sample lesson on teaching trigonometry in presentation format.

I created a worksheet for the activities on classifying and dissecting polygons. Click the link.


6 thoughts on “Trigonometry – why study triangles”

  1. This 25 Polygons page is also something I’ve shared with tertiary faculty.

    Visual analysis is a skill that many students with a Geometric “bent” have.

    Those whose inclination is purely Numeric, may find this task challenging.

    I have seen 6th graders who were non-native speakers of English complete tasks like this quickly. While those who always had their hands up with “right answers” to numeric questions were frustrated when asked to solve a geometric problem.

    I found this interesting. Wondering why Numeric kids might hit the wall in Algebra (symbolic) and Geometry (visual).

  2. If I give s simple tri gproblem where one angle (other than the right angle) and one side are known, they obviously have to use trig to find one of the other sides.

    But do you think it’s overkill to use a trig ratio to find the third side or to just use a2 + b2 + c2?

    In any case, I made a silly trig video that I put on YouTube.

    I use a2 + b2 = c2 to find the last side but I feel guilty that it’s not a trig video through and through! But is it overkill?

    1. I think P.T is as trig as it is as geometric and as algebraic concept. I think it’s best to call your video ‘solving triangle video’ rather than the more general trig video.

      I think the best is to present in the video that while the first two sides can be solved by ideas of trig ratio (actually there are other ways, e.g constructing similar triangles then use ratio and proportion or by scale drawing) the third side can be solved by trig and by P.T. I would consider it an overkill if students will be required to always use these two to solve the third side. They should know that both works. So when should they use this solution? I think that depends on the given number and the available calculator. The more keys needed to solve the problem, the greater the probability of getting incorrect answer.

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