+0  
 
0
623
4
avatar

sinΘ ≈Θ

Guest Aug 9, 2014

Best Answer 

 #3
avatar+94118 
+8

I'd like to take Alan's explanation and expand upon it a little.

NOTE: THIS IS ONLY TRUE AS THE ANGLE TENDS TO 0

   $$The circumference of a circle is $2\pi r$\\
If the radius is 1 unit then the circumference is $2\pi$\\
So if the angle is measured in radians then the arc length will be equal to the angle that it is subtended from. This is for a unit circle.\\\\$$

 

Melody  Aug 9, 2014
 #1
avatar+4472 
0

AzizHusain  Aug 9, 2014
 #2
avatar+27229 
+5

The following images might help:

theta

theta2

So sin θ ≈ θ only when θ is small

Alan  Aug 9, 2014
 #3
avatar+94118 
+8
Best Answer

I'd like to take Alan's explanation and expand upon it a little.

NOTE: THIS IS ONLY TRUE AS THE ANGLE TENDS TO 0

   $$The circumference of a circle is $2\pi r$\\
If the radius is 1 unit then the circumference is $2\pi$\\
So if the angle is measured in radians then the arc length will be equal to the angle that it is subtended from. This is for a unit circle.\\\\$$

 

Melody  Aug 9, 2014
 #4
avatar+92788 
+5

Here's the proof of this using the "Squeeze Theorem".....it's somewhat complicated, but if you have some patience, I think you will appreciate the geometry involved. The proof is the first one on the page.

http://tutorial.math.lamar.edu/Classes/CalcI/ProofTrigDeriv.aspx

Thanks to Paul's Online Math Notes for this one.....(I certainly couldn't have derived it!!!)

BTW....."Paul" is Dr. Paul Dawkins...he's a professor at Lamar University in Texas

 

  

CPhill  Aug 9, 2014

17 Online Users

avatar
avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.