#trigonometric functions

HERES ALL OF THEM IN ONE:

Tan and Cot are fraternal twins, each acting as an older sibling/parent figure to Sin&Cos and Csc&Sec respectively. Sin and Cos are like siblings, although they are not related. Csc and Sec are cousins!!

My pairings are not quite accurate also, so I’d like to redo here:

Sin -> Cos, Csc

Cos -> Sin, Sec

Tan -> Cot, Sec

Cot -> Tan, Csc

Csc -> Sec, Cot, Sin

Euler's Identity and the 3D unit helix

Sine and cosine are the 2D projections of the unit helix.

When I first saw the concept of the unit helix some years ago, trigonometric functions made so much sense.

Unfortunately, I never heard of any of it in school. Trigonometry was taught as a very unintuitive thing, as something one could not have a connection towards, as something not really 'integratable' into one's own mind. There were no elaborations about 'why' equations are the way they are, nor how the methods are used in relation to the "why", and what these methods are in concrete - in a manner which can be plotted in one's own imagination.

The abstraction appeared alienated from the own thinking process. No inner comprehension was really possible.

Yet, seeing only this concept with no further words added, it was an "Eureka-moment" for me.

Do you have hints for stuff regarding calculus that made you get the eureka moment in your brain? If you do pleeease tell me the source(s)!

(I enjoy it.) Wish I had bigger paper and a ruler/ trig function ruler right now and a 4 color pen ( i have all these components at home, but I am in the clinic rn D:

I need to write a list of what I will do today when I get back home:

(Doing now because now or never...)

- find rulers, the 4 color pen, find large paper and sticky tape > put that in my backpack

-eventually re-dye my hair glowingly orange today, if the time is left (between all the nerd activities and procrastination ha)

- changing a segment in a piece of jewelry I assembled yesterday (an opal pendant with large holes, adding a large segment clicker around instead of an ugly key ring, and then adding the tiny klein bottle pendant to it.