So the theta that is the input into sine is from the rotation of the side of the triangle inside the Unit Circle that has a constant length (still talking about the side of the triangle) that is the radius of the circle?
Yes exactly. Or another way to out it, the theta represents the rotation angle that arises from the positive x-axis and terminates at the particular radius.
@@fredkong6671 Thanks for confirming that! For software engineering and shader programming that can actually be applied so I am thankful that I generally understand the most important parts of Trigonometry now! Thanks again!
Extremely valuable for helping my 1st level electrician students visualize the relationship. If I may ask, how is the animation produced? Please don't tell me you wrote it from scratch. 😩 I'm looking for something that would allow me to control the angle arbitrarily in real time. A lot of my instruction has had to move online in the age of Covid and it can be tough to hold students' attention with my crude graphic tablet + software whiteboard sketches.
I'm glad the animation is helpful for your students. I used desmos to create the animation. It's easy to use and very intuitive. I have attached a link to the animation and encourage you to modify it for your own use. Please let me know if you have any other questions! Here is the link: www.desmos.com/calculator/9wxznmorjc
I do not have the file anymore, but I just used polar coordinates on Desmos. You can simply define your circle by naming its radius. You can also establish a parameter that is common to both the sine function and a point moving in a corresponding manner around the unit circle. I believe you can also find a file by searching “unit circle” and “Desmos”. Good luck!
So basically the diff between output of sine and cosine is: If the input starts at zero and increases linearly, then sine output starts at origin and cosine output starts at x=0, y=1?
![Skilla Baby - Misfit (Feat. Polo G) [Official Video]](http://i.ytimg.com/vi/IjsylSnNMyw/mqdefault.jpg)
This is one of the videos that visualises the sin cos function very well..Thank you
This video goes crazy!!! One of the best I've seen so far explaining this topic!! I immediately subscribed, from one Math Educator to another!
Welcome aboard!
Thank you so much for the graphs in motion! It is like cause and effect happening at the same time visually! The process is so clear!
Thanks for the feedback! It’s always helpful to be able to see concepts in action!
This video is really, really good. I totally understand the relation now.
Thanks for the vote of confidence. I’m glad it was helpful!
Thanks for posting a video clarifying why a linear increase in input to a sine function oscillates.
I like the way you put that!
Excellent visualization sir
Thank you!
Thanks, for your explaining
Glad it was helpful!
My mind is blown. Thanks for the video
You’re welcome!
Amazing explanation sir🎉❤thank you so much😊🎉
You’re welcome! Glad it helped you!
Amazing...
Thank you!
Thank you.
You're welcome!
Fred, are you willing to share that DESMOS graph?
I teach Precalculus and that was pretty damn cool!
Thanks sir
You’re welcome!
So the theta that is the input into sine is from the rotation of the side of the triangle inside the Unit Circle that has a constant length (still talking about the side of the triangle) that is the radius of the circle?
Yes exactly. Or another way to out it, the theta represents the rotation angle that arises from the positive x-axis and terminates at the particular radius.
@@fredkong6671 Thanks for confirming that! For software engineering and shader programming that can actually be applied so I am thankful that I generally understand the most important parts of Trigonometry now! Thanks again!
Extremely valuable for helping my 1st level electrician students visualize the relationship. If I may ask, how is the animation produced? Please don't tell me you wrote it from scratch. 😩 I'm looking for something that would allow me to control the angle arbitrarily in real time. A lot of my instruction has had to move online in the age of Covid and it can be tough to hold students' attention with my crude graphic tablet + software whiteboard sketches.
I'm glad the animation is helpful for your students. I used desmos to create the animation. It's easy to use and very intuitive. I have attached a link to the animation and encourage you to modify it for your own use. Please let me know if you have any other questions! Here is the link: www.desmos.com/calculator/9wxznmorjc
@@fredkong6671 Sweet, thanks so much.
Beautiful. How can one visualise calculus?
Stay tuned for a calculus visualization video!
❤❤
"Terminal" is the side of the triangle that is a constant length that is the radius of the Unit Circle, right?
Correct!
@@fredkong6671 Saw now. Apologies for the delayed reply! Thanks for for confirming that!
Would you be willing to share your Desmos Graph? I'm baffled how you drew a purple curve from 0,0 to the sine point.
I do not have the file anymore, but I just used polar coordinates on Desmos. You can simply define your circle by naming its radius. You can also establish a parameter that is common to both the sine function and a point moving in a corresponding manner around the unit circle. I believe you can also find a file by searching “unit circle” and “Desmos”. Good luck!
Could you please let us know what application you use to visualize these functions?
Yes, this is the Desmos graphing tool available at Desmos.com.
Thank you very much. 🙏
So basically the diff between output of sine and cosine is: If the input starts at zero and increases linearly, then sine output starts at origin and cosine output starts at x=0, y=1?
Right again!
@@fredkong6671 Great! Thanks!
X...Y...2 overlapping oscillating curves...DNA...logical progression.
Yes, I like the double helix comparison!
❤️🌷
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