Want to talk about unit circle

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Discussion Overview

The discussion revolves around the reasons for using the unit circle in defining sine and cosine functions. Participants explore the implications of this choice and seek guidance on sharing additional insights and external sources related to the topic.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant expresses a desire to understand why sine and cosine functions are defined using the unit circle specifically, rather than circles of different radii.
  • Another participant notes that the sine and cosine functions correspond to the y and x coordinates of points on the unit circle, suggesting this as a fundamental reason for the choice.
  • A participant mentions that using a unit circle simplifies formulas by avoiding additional factors from other radii.
  • Some participants inquire about sharing their own research and external sources, indicating a willingness to contribute further to the discussion.

Areas of Agreement / Disagreement

Participants generally agree on the utility of the unit circle for simplifying formulas, but the discussion remains open regarding the broader reasons for its use and the implications of defining trigonometric functions in this way. There is no consensus on the completeness of the reasons presented.

Contextual Notes

Participants express uncertainty about the best way to share their findings and whether external sources can be included in the discussion.

Who May Find This Useful

Individuals interested in trigonometry, mathematical definitions, and the rationale behind the use of the unit circle in mathematics may find this discussion relevant.

Jessica01
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Hi all,

I was wandering on the web to collect some solid and justifiable reasons to answer a question "Why we always choose a unit circle."? I saw several websites and meanwhile I saw this post https://www.physicsforums.com/threads/trig-unit-circle-why.475575/. I saved it. But overall, I couldn't get some good set of reasons, I then collected some reasons, prepared an article and came here today but couldn't see an option to submit my own reply, don't know why it's happening with my account.

However I want to share that article here. Any advice on should I copy paste it here or what? It's live on a blog. Please reply. Thank you.
 
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Jessica01 said:
Hi all,

I was wandering on the web to collect some solid and justifiable reasons to answer a question "Why we always choose a unit circle."? I saw several websites and meanwhile I saw this post https://www.physicsforums.com/threads/trig-unit-circle-why.475575/. I saved it. But overall, I couldn't get some good set of reasons, I then collected some reasons, prepared an article and came here today but couldn't see an option to submit my own reply, don't know why it's happening with my account.

However I want to share that article here. Any advice on should I copy paste it here or what? It's live on a blog. Please reply. Thank you.
The post in the link above is closed, so you can't reply to it. I didn't look at all the posts in that thread, but I suspect that it was closed automatically due to its age.

The reason for using the unit circle is that the sine and cosine functions are defined as the y and x coordinates, respectively, of points on the unit circle. There's not a whole lot more to it than that.
 
Thank you for the prompt response Mark! But my question is still there, why we define sine and cosine functions of points on unit circle? Why NOT on circle with radius 2 or 1/4 etc? I did well research on the web and gathered several reasons in detail. I can't wait to share them here. That's why I asked before as well, please guide me how I can share it here?
 
Jessica01 said:
Why NOT on circle with radius 2 or 1/4 etc?
It makes formulas simpler not to have a factor of 2 or 1/4 in them.
 
Hmmm yeah it is one of great reasons. I've some other reasons as well. Should I share them here? Is there any issue of sharing external sources? I'm new to this forum so please guide me.
 
Jessica01 said:
Hmmm yeah it is one of great reasons. I've some other reasons as well. Should I share them here? Is there any issue of sharing external sources? I'm new to this forum so please guide me.
What do you have in mind?
 

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