How do you generate math figures for academic papers? Good day! I am looking for any tool that would allow me to generate a figure similar to the figures embedded in the paper by King et al. (2020) titled "Trigonometry: a brief conversation."
King, C., Evelyn, T., Ye, F., & Carvajal, B. (2020). Trigonometry: A Brief Conversation. Open Educational Resources. https://academicworks.cuny.edu/qb_oers/167/
 A: I find Inkscape a bit too heavy and use a much smaller vector drawing program for Windows called Mayura Draw in combination with equally antiquated psfrag package.
A: TikZ (a self-referential acronym for Tikz Ist Kein Zeichenprogramm) is an excellent, and extremely versatile drawing program. I highly recommend it.
There's an extensive manual. It might be frightening at first sight, but it in fact starts very gently, with a long list of worked examples (starting on page 30).
There's also some humorous examples of things not to do when designing a graphic (check out the stuff around page 99).
A: To complement Kostya's answer, here is a way to turn hand-drawings into something looking vaguely professional using inkscape, very quickly (and for free).

*

*Draw something on paper.

*Take a photo in good light conditions, and drag the photo file into inkscape.

*Select the photo in inkscape and press Shift + Alt + B at the same time (this starts the bitmap function).

*Tweak the parameters until you're happy with them (click "update" to preview), then click "OK".

*Delete the underlying image, an svg (vector graphics) picture will have been generated on top of it.

*Go to "document properties" to tweak the page size.

*Press Ctrl + Shift + E to open the export function, and export it.

*You get an image (png or jpg) which you can include using various packages into a LaTeX file.

This gives the middle image (the above process took ~10 seconds):

Because it's an svg file, you can use the node tool (select the line drawing, then press N) to tweak the image a bit, change its colour, etc., e.g. giving the above picture on the right.
Here is another example, based on a random maths drawing I found online. The last one took about a minute to (badly) edit.

Tip: do not delete the inkscape file, so that you can re-edit the image later if you like.
A: In the case you prefer to draw pictures on a computer without entering the source code manually, I recommend Inkscape, which is a free, opens source vector graphics editor. It has a Latex plugin that allows you to include math formulae, as well as a variety of other tools.
It outputs an .svg file, which is essentially an .xml document describing your graphics, so in principle it can be edited by a human. Also, many programming languages have tools to create .svg files, e.g., the swgwrite package in Python. Computer algebra systems allow one to save their graphics in .svg, that can then be edited in Inkscape.
For conversion between Tikz and .svg, see e.g. here or here.
