43524004530 http://1ucasvb.tumblr.com/post/43524004530/drawing-process-for-the-sine-function-since 108 Drawing process for the sine function Since...

Drawing process for the sine function

Since people were really interested on the sine function in that previous image, I figured I’d post this one as well. It will explain things better.

This is what the sine function of the circle actually means: it’s the y-coordinate associated with the arc length, shown in blue. A circle has circumference 2·pi·r. The unit circle has radius 1, so the full unit circle has circumference (or arclength) 2·pi.

The blue arc and the blue line shown at right have exactly the same length. This is the angle in radians.

This is the geometric definition, though. A much more powerful definition is based on infinite series.

(For the polygonal trig functions, I kept the idea of an angle around the polygon, but I gave up on the idea of using the length around the polygon - its perimeter. This caused a lot of confusion about why the side of the square didn’t trace a straight line.)

1. animewhenwet reblogged this from 1ucasvb
2. floatingintrees reblogged this from 1ucasvb
3. morningmercies reblogged this from the-studentteacher
4. vietyen reblogged this from 1ucasvb
5. omori-senpai reblogged this from 1ucasvb
6. ijoshuakelley reblogged this from metinseven
7. stuckinthewrongyear reblogged this from metinseven
8. metinseven reblogged this from 1ucasvb and added:
Math is more fun when presented visually.
9. megal0punny reblogged this from 1ucasvb
10. swimminghere reblogged this from 1ucasvb
11. doobsterusmaximus reblogged this from 1ucasvb and added:
it’s like music to my brain
12. nopanicnoheatbae reblogged this from 1ucasvb
13. lu-fu-nope reblogged this from 1ucasvb
14. andersonrandom reblogged this from le-mec
15. hummusapiens reblogged this from 1ucasvb
16. donkinator reblogged this from xyvch
17. xyvch reblogged this from 1ucasvb
18. sydneybehning reblogged this from 1ucasvb