Want to talk about unit circle

In summary, the conversation discusses the reasons for always choosing a unit circle in trigonometry. One main reason is that the sine and cosine functions are defined as the y and x coordinates of points on the unit circle. This makes formulas simpler and avoids having factors of 2 or 1/4 in them. The original poster has additional reasons to share and is asking for guidance on how to do so on the forum.
  • #1
Jessica01
3
0
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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  • #2
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.
 
  • #3
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?
 
  • #4
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.
 
  • #5
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.
 
  • #6
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?
 

1. What is the unit circle and why is it important?

The unit circle is a circle with a radius of 1 unit, centered at the origin on a graph. It is important because it helps us understand and visualize the relationships between angles and trigonometric functions such as sine, cosine, and tangent.

2. How do you plot points on the unit circle?

To plot points on the unit circle, we use the coordinates (x,y) where x is the cosine of the angle and y is the sine of the angle. For example, the point (cos30°, sin30°) would be plotted at the coordinates (0.87, 0.5) on the unit circle.

3. What is the connection between the unit circle and radians?

Radians are used to measure angles on the unit circle. One radian is equal to the length of the arc on the unit circle that subtends an angle of 1 radian. This means that the circumference of the unit circle is equal to 2π radians.

4. How does the unit circle relate to trigonometric identities?

The unit circle is used to derive and understand trigonometric identities. By plotting points on the unit circle, we can see the relationships between the trigonometric functions and how they are related to each other.

5. Can you explain the concept of reference angles on the unit circle?

Reference angles are angles formed between the terminal side of an angle and the x-axis on the unit circle. They are always positive and are used to find the exact values of trigonometric functions for angles greater than 360°. Reference angles can also be used to simplify calculations involving angles in radians.

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