What Sine and Cosine Have to do with the Unit Circle

  Рет қаралды 4,192

Caramel Productions

Caramel Productions

2 ай бұрын

This video is my capstone project for my high school! I created this animation in the engine Manim by Grant Sanderson, which allowed me to write Python code to produce mathematical visuals. My Python file totaled to 825 lines of code. You can view the file as a python file or pure text file at this link: drive.google.com/drive/folder...
This project took me many, many hours of work, including learning how to program in Manim in the first place.

Пікірлер: 11
@D.C.7.3
@D.C.7.3 2 ай бұрын
love this, such a great explanation
@adamamir8554
@adamamir8554 2 ай бұрын
One of the most interesting and amazing math videos that I have seen.
@carameldotzip
@carameldotzip 2 ай бұрын
Thank you so much!
@T0NYD1CK
@T0NYD1CK Ай бұрын
Another take: Ignore trigonometry! Sines and cosines are known as "circular functions". Also, ignore angles in degrees, in fact, ignore angles altogether! Just use the arc length from the x-axis anti-clockwise round the circle. Sine comes from a word meaning arc or curve. When a point moves round the curve it has a certain distance from the x-axis. That distance is the sine of that arc length. Cosines, as the name suggests, accompany sines and the cosine is the horizontal distance from the point on the arc to the y-axis. Tangent implies touching and the line through the point that touches the circle has a length between the point and the x-axis. That is the tangent of that arc length. The distance between the point and the y-axis is the cotangent. Secant implies cutting and the line that cuts the circle along the x-axis has a length between where the tangent meets the x-axis and the y-axis equal to the secant of the arc length and, yes, the cosecant is at right angles to that. All the trig stuff, including some trig identities, now follow by using similar triangles
@user-pc9ql2fd6f
@user-pc9ql2fd6f 2 ай бұрын
Excellent voice and animations
@Joe-by3ez
@Joe-by3ez 2 ай бұрын
Excellent information and very interesting
@juriG10
@juriG10 2 ай бұрын
Excellent Job
@joandarc1609
@joandarc1609 2 ай бұрын
slay queen
@movingshapes
@movingshapes 21 күн бұрын
Good video. I am gonna use it on a trigo class soon :)
@juriG10
@juriG10 2 ай бұрын
If you have done this (without Steeling the Animations) you are severely underratet
@carameldotzip
@carameldotzip 2 ай бұрын
Thank you so much! I will totally admit that I referenced another creator’s unit circle to make mine more readable, but all of the code for this video is wholly my own. Your support is so thoughtful and I’m ecstatic that you enjoy this!
Trigonometry Concepts - Don't Memorize! Visualize!
32:35
Dennis Davis
Рет қаралды 2,7 МЛН
小路飞姐姐居然让路飞小路飞都消失了#海贼王  #路飞
00:47
路飞与唐舞桐
Рет қаралды 94 МЛН
ONE MORE SUBSCRIBER FOR 6 MILLION!
00:38
Horror Skunx
Рет қаралды 13 МЛН
Как быстро замутить ЭлектроСамокат
00:59
ЖЕЛЕЗНЫЙ КОРОЛЬ
Рет қаралды 9 МЛН
Dynamic #gadgets for math genius! #maths
00:29
FLIP FLOP Hacks
Рет қаралды 18 МЛН
What does the second derivative actually do in math and physics?
15:19
All of TRIGONOMETRY in 36 minutes! (top 10 must knows)
36:50
JensenMath
Рет қаралды 193 М.
This pattern breaks, but for a good reason | Moser's circle problem
16:13
Learn Unit Circle Radians in LESS THAN 5 MINUTES!
4:51
Does Math for Coffee
Рет қаралды 26 М.
All 6 Trig Functions on the Unit Circle
8:19
Beautiful Math
Рет қаралды 1,3 МЛН
Light sucking flames look like magic
18:05
Steve Mould
Рет қаралды 1,6 МЛН
The Easiest Way to Memorize the Trigonometric Unit Circle
9:48
Professor Dave Explains
Рет қаралды 234 М.
The Most Beautiful Equation
13:39
Digital Genius
Рет қаралды 501 М.
Cars VS King Kong 🚗 | BeamNG.drive #shorts
0:57
DriveTrickX
Рет қаралды 68 МЛН
Cars VS King Kong 🚗 | BeamNG.drive #shorts
0:57
DriveTrickX
Рет қаралды 68 МЛН