The Soh Cah Toa Ravings Of a Quarantined Mathematician

Being quarantined during these unprecedented times can present both challenges and opportunities. For mathematicians, this period can provide a unique chance to dive deep into their research, explore new concepts, and let their minds wander freely without the usual distractions. In this article, we delve into the world of a quarantined mathematician and unpack their ravings on the fascinating topic of Soh Cah Toa.

If you've ever taken a trigonometry course or dabbled in geometry, you may have come across the term "Soh Cah Toa." What does it mean? Well, it's a mnemonic device used to remember the three most important trigonometric ratios: sine, cosine, and tangent. Each of these ratios is defined based on the lengths of the sides in a right-angled triangle.

Sine - The Sensational Ratio

Our quarantined mathematician went on a raving spree about the wonders of the sine ratio. They explained that the sine of an angle in a right-angled triangle is equal to the length of the side opposite the angle divided by the length of the hypotenuse. This ratio is captivating because it gives insights into the relationship between angles and ratios of the sides. The mathematician claimed that the sine ratio provides a gateway to understanding the periodic nature of many phenomena.

SOH-CAH-TOA: Ravings of a quarantined mathematician

by Adam Hrankowski(Kindle Edition)

5 out of 5

Language	:	English
File size	:	9141 KB
Text-to-Speech	:	Enabled
Screen Reader	:	Supported
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As they delved further into their musings, our mathematician continued to extol the virtues of the sine ratio. They revealed its role in the study of sound waves, oscillations, and even celestial mechanics. It turns out that the sine function plays a crucial role in describing various natural phenomena, thus leaving our quarantined mathematician in awe of its beauty.

Cosine - The Classy Ratio

The cosine ratio also captured our mathematician's imagination during their bouts of quarantine-induced ramblings. They explained that cosine is the ratio between the length of the adjacent side and the hypotenuse in a right-angled triangle. It was awe-inspiring for them to realize how this ratio is intimately connected to the concept of similarity in triangles.

But the real excitement for our mathematician lay in the rich applications of cosine. They illustrated how the cosine function can be used to model periodic phenomena that have a phase shift from the sine function. Our quarantined mathematician diligently embarked on new research projects, utilizing cosine in everything from analyzing the behavior of pendulums to predicting the movement of ocean waves.

Tangent - The Thrilling Ratio

Tangent, the final component of Soh Cah Toa, became the pinnacle of excitement for our mathematician. They described it as the ratio between the length of the opposite side and the adjacent side of a right-angled triangle. For them, the tangent ratio unraveled a treasure trove of mathematical delight.

Our mathematician fervently explored tangent's connection to slope and rates of change. They used it to analyze the steepness of ramps, the incline of roller coasters, and the curves of bridges. The quarantine gave our mathematician the luxury of time to fully absorb the intricacies of tangent, leading to many surprising discoveries.

As the quarantined mathematician raved and rambled about Soh Cah Toa, their enthusiasm was contagious. They showcased how these trigonometric ratios are the building blocks for understanding and modeling various real-world phenomena. The quarantine became an opportunity for our mathematician to reset, refocus, and truly appreciate the beauty and power of mathematical equations.

So, the next time you come across Soh Cah Toa, don't dismiss it as a mere acronym. Remember the fervor of the quarantined mathematician, and let their ravings inspire you to dive deep into the world of trigonometry and beyond.

SOH-CAH-TOA: Ravings of a quarantined mathematician

by Adam Hrankowski(Kindle Edition)

5 out of 5

Language	:	English
File size	:	9141 KB
Text-to-Speech	:	Enabled
Screen Reader	:	Supported
Enhanced typesetting	:	Enabled
Print length	:	129 pages
Lending	:	Enabled

FREE

Have you ever wondered:

• What's a mathematical algorithm for efficiently choosing a spouse?

• How does your running style affect your perspective of current events in the Andromeda Galaxy?

• Is spaghettification an actual word?

Wonder no longer! All is revealed in this compendium of articles, written almost entirely during the Covid 19 lockdown of spring 2020. Originally published on medium.com, this variety of mathematical meanderings provides rare insight into a mind obsessed with:

• finding infinite series for transcendental functions with (almost) no calculus.

• ranting about mathematics education.

• stretching, sliding, twirling and curving the number line.

Perfect bathroom reading to distract you from the fact that you still don't have any toilet paper.