Math Education Concepts

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Teaching Inverse Trigonometric Functions

Inverse trigonometric functions are functions that reverse trigonometric functions (in brief).  Trigonometric functions are functions of an angle measure.  They are primarily used to find lengths of the legs of a triangle (or some triangular relationship).  Inverse trigonometric functions are functions of the ratio of lengths of a triangle.  They are primarily used to find the corresponding angle of the ratio of the legs of a triangle.  There are other uses, but I will keep it brief for this blog.

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Every semester, I have to put more effort into explaining inverse trigonometric functions.  Although the concept is the same, the students, and their perceptions, change.  There are only so many ways I can think of to explain this concept.  So I decided to get some help from several online resources.  Of course, I suggest that my students do the same, but that’s another blog, for another day.

Here are a few links I came across that should be helpful to students and teachers alike, looking for alternative ways to explain inverse trigonometric functions.


Khan Academy

Randy Anderson (YouTube)

Paul’s Online Math Notes (Paul Dawkins)

How do you teach inverse trigonometric functions to your students?



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Applications of Trigonometric Functions

Trigonometric functions are functions of angles and are useful for finding the lengths of the sides and measures of the angles of triangles (primarily right triangles).  They are also useful for describing harmonic or periodic motion, such as sound waves.

Most students either love or despise trigonometric functions.  I happen to enjoy them.  They are mysterious, yet simplistic functions.  When you get them, you get them!!!

When teaching the trigonometric functions, I approach them in one of two ways: using right triangle trigonometry (the most common) or using components of the slope of a line (rise, run, slope), etc.  I recently started using the second approach to see if students new to trigonometry would understand the functions easily.  I’m still working that out.








Trigonometric functions are applied in astronomy, geography, engineering, physics, and architecture.  Here are a few examples:

  1. Distance between planets
  2. Height of mountains
  3. Dimensions of land

The history of trigonometry tells me that it all started with the “stars” or spherical geometry.  Linear algebra followed and we now have a very comprehensive system that revolves around the trigonometric functions.  Every semester, I learn something new about these functions and make a note to myself to learn more!

NOTE: This blog does no justice for the true value of trigonometric functions.  My goal here is to inspire you to research trigonometry for yourself and find out why they are so intriguing.

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