Strategies for Teaching Trigonometry

Various topics in trigonometry are covered in the mathematics curriculum throughout high school. In grade 10 students are introduced to similar triangles, right angle trigonometry and the sine and cosine law to calculate missing angles or side lengths. In grade 11 and 12 trig concepts become even more prevalent and abstract involving topics such as the ambiguous case, trigonometric identifies and the graphing and transformations of trigonometric functions.

In an earlier blog post I discussed the use of spaghetti to produce a graph of the sine function, which was one activity to make trigonometry more hands on. In this post I will discuss a few more options that can make trig a little more hands on within the classroom.

One of the ways trig can be used within the classroom is to look at Pythagorean's theorem and ride angle trigonometry. All you need is some tape, protractors, measuring sticks and square floor tiles. Students can use the tape to cover the gaps between multiple floor tiles, if the tape goes over 4 tiles then the length of that side will be 4. The tap can be used to create a right angle triangle where the length of each side is visually determined by how many squares the tape crosses. The math involved here will be with the angle and the hypotenuse side length as it goes diagonally through multiple squares, making an exact length calculation difficult. Students can measure the lengths of each side with a meter stick or calculate the length of the missing side using Pythagorean's  Theorem. The angle can also be determined using a protractor. Various groups within the classroom can create triangles of different size and record their results to share with other groups. After each group has created a triangle and calculated their missing variables a class discussion can be had about the results discussing how different size triangles effects the angles.

 

Image retrieved from: https://www.teachengineering.org/activities/view/nyu_triangles_activity1

Trigonometric identities, another trig topic seen in the senior level classes, are often infamous among students for being one of the more challenging topics. My goal within my classroom would be to eliminate that stigma against trig identities by creating a classroom culture where student's know its okay to be wrong sometimes, what's important is that you learn from your mistakes and move on! Which is why its important to tell students with trig identities that they require lots of trial and error sometimes, they don't always work out perfectly the first time which is perfectly okay. Another good way to introduce identities is by using non-trig examples first such as:

3x + 4 = 7

Hopefully these strategies can help eliminate the stigma in our classrooms surrounding trigonometry and make the topics fun and intriguing for all the different types of learners in our classrooms!