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:

- Distance between planets
- Height of mountains
- 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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