How To Intuitively Understand Sin And Cos?

These concepts are hilariously simple!

Hemanth
Street Science

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How To Intuitively Understand Sin And Cos? — An illustration showing a circle with its centre at (0, 0) of a cartesian coordinate system. Below this circle, the following question is written: “Cos & Sin??”
How to intuitively understand Sin and Cos — Illustration created by the author

The concepts of Sin and Cos appear in a variety of places in mathematics and science. Yet, many folks struggle to understand why we need these concepts.

Take mathematics involving frequencies for instance. How are the notions of Sin and Cos related to frequencies? Well, by the end of this essay, you will laugh about how simple the relationship actually is.

I remember when I first encountered these concepts as part of “trigonometry”. It was a nightmare for me; I think that in most cases, issues start arising when one distances oneself away from first principles.

“Trigonometry” is just a fancy word for the branch of geometry that deals with triangles. To intuitively understand Sin and Cos, we don’t even need trigonometry. All we need is its parent: geometry; more specifically, one particular geometry.

If you think about it, everyone has an innate understanding of geometry. All folks can grasp what a circle is, regardless of their technical abilities. A circle is all that we will need to intuitively understand Cos and Sin. Let us begin.

The Magic of the Unit Circle

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