Want to talk about unit circle

AI Thread Summary
The discussion centers on the reasons for using the unit circle in trigonometry, particularly why sine and cosine functions are defined based on it. The unit circle simplifies formulas by eliminating additional factors, making calculations more straightforward. The original poster expresses a desire to share their research on the topic but is unsure how to do so due to account issues. Participants encourage sharing external sources and insights, emphasizing the importance of clarity in mathematical definitions. Overall, the conversation highlights the educational value of understanding the unit circle's role in trigonometry.
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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