# Questions tagged [trigonometry]

For questions about effectively motivating and teaching the concepts of trigonometry, including the unit circle, the sin/cos/tan functions, and other related ideas.

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### Phase shift vs. horizontal shift, and frequency vs. angular frequency in sinusoidal functions

TL;DR version: It seems to me that high school curricula no longer distinguish between "horizontal shift" and "phase shift", or between "frequency" and "angular ...
673 views

### Interesting Trigonometry problems

After explaining some basic trigonometry to my kid, such as $\sin (\alpha+\beta) = \sin \alpha \cos \beta + \cos \alpha \sin \beta$, Law of sines, Law of cosines, I wonder if there are some ...
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### How to motivate the geometric definition of trigonometric functions on the unit circle

Suppose your students know already the geometric definition of $\sin$ $\cos$ and $\tan$ for angles between $0^{\circ}$ and $90^{\circ}$. How can I motivate the definition of $\sin$, $\cos$ and $\tan$...
2k views

### Proving trigonometric identities

When teaching trigonometric identities, I found the students had trouble proving them. All the students taking turns to ask almost all the questions of an exercise embarrased me somewhat. In order to ...
170 views

### Trigonometric ratios

How should I teach students the trigonometric ratios who are indeed studying trigonometry for the first time in their life? The course has said that there are six ratios based on sides in a triangle ...
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### Unit circle vs. ratios of right triangles vs. wave functions for introducing trig functions

In an introductory trignometry course, there are many options for introducing trigonometric functions: As ratios of sides of right triangles As coordinates (or ratios of coordinates) of intersections ...
3k views

### Why are degree angle-measurements taught?

Apologies if this question has some obvious answer. Why are degrees still taught as a measure for angles, to be replaced later by radians (probably confusing many people), rather than just starting ...
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### The best way to introduce trigonometric functions in a rigorous analysis course

This is something I have always had issues with. Generally, three approaches are used: The geometric path: this follows the standard way how you would introduce these functions in school. The problem ...
Tau ($\tau = 2 \pi$) has more merits in its application, but pi is the established standard in industry and education. Is the trade-off of teach-ability of circle concepts worth the subsequent ...