I couldnt see your work, it says 'unauthorized', maybe you didnt make it public?
Actually i totaly go random with colors but its nice coincidence :) I really like it!
And about graphs of functions; yes! arriu suggested the same below, and this graphic from wikipedia is a good reference point for me, thanks! I have an idea to how to visualize graph of functions from unit circle to make it simple to understand! Will start to work on it in next week i hope.
Thanks for great suggestion, and if you make your work public i really would want to see it!
Your work is absolutely briliant and gave me idea to draw theta angle like you did! Also i'm gonna include an option to draw values of lines in canvas.
For some mental fun, try these values for the angle and see what observations you can make about the results:
76.34541
126.869896
137.50777
However, I find it a bit bothersome that the input field doesn't properly accept floats, and the floats get rounded unnecessarily. Please don't do that, or have an option to customize it.
Also, you miss the more obscure trigonometry values:
You're right! I've added a new section named 'general options' and 'rounding numbers' option under it to you can disable rounding. I hope it helps, if not please tell.
And thanks about other great suggestions, those are really interesting. I'll check and try to bring them into party!
Very nice! I had a trig teacher years ago that taught only using formulas, without showing or explaining the unit circle. It was so confusing, hated the class until I discovered the unit circle diagram like this, then it all made much more sense.
That was my exact motivation while making this! This visualization helps me alot to understand trigonometry so i think it will be good to make a sandbox out of it. I hope this helps somebody who trying to understand basics of trigonometry.
Interesting fact, the sine is a mistranslation of the original Arabic abbreviation jb, which itself is a transliteration of the Sanskrit word for half the chord, jya-ardha. Basically the original translator they thought that the word was jaib ("bosom"), which was then translated to sinus which means much the same word.
So our most famous and important trig term is basically an error.
> A hiding-place, place of concealment: ut in sinu gaudeant, gloriose loqui desinunt, qs. in their bosoms (or, as we say, in their sleeve), i. e. in secret, Cic. Tusc. 3, 21, 51; “so of secret joy,” Tib. 4, 13, 8: “in tacito cohibe gaudia clausa sinu,” Prop. 2, 25 (3, 20), 30; Sen. Ep. 105, 3; cf. “also: plaudere in sinum,” Tert. Pudic. 6: suum potius cubiculum ac sinum offerre contegendis quae, etc., the secrecy or concealment of her bed-chamber, Tac. A. 13, 13: “abditis pecuniis per occultos aut ambitiosos sinus,” i. e. in hiding places offered by obscurity or by high rank, id. H. 2, 92.—
But those examples make it pretty clear that the sense of sinus is secrecy, not emptiness. Presumably this comes from the idea that you can hold ideas and opinions within your heart (in your breast, sinus) and no one else can see them.
Interesting, I have always visualized tangent differently. A line perpendicular to the X axis that stops at the intersection with the extension of the radius line.
I also always used the perpendicular to x-axis version, but I like this version better bcs the tangent tangents in the point of interrest, plus cotangent and tangent are colinear
Wow...I never actually knew the significance of secant and cosecant, or how tangent/cotangents' lengths were related to the unit circle and right triangle. I knew the formulas to calculate them, but not really what they truly meant.
My only comment is that while canvas is certainly effective, if you built it in SVG you would only need to animate the points and not draw the whole thing each time step. Admittedly not a big saving though.
Thanks! Happy to see you like it! And you're right about SVG, but i have plans to draw additional things also, like graphics of functions, so im not sure if SVG would be flexible as canvas. (or i can use it effeciently :))
The color schemes we used are similar, I kind of copied mine from this image on Wikipedia: https://en.wikipedia.org/wiki/Trigonometric_functions#/media... I wonder if the author of this site did the same?
What would be REALLY cool would be a connection between this diagram and the graphs of the functions: https://en.wikipedia.org/wiki/Trigonometric_functions#/media...
something like this: https://www.geogebra.org/m/cNEtsbvC