The Open Door Web Site
HOME PAGE BIOLOGY CHEMISTRY PHYSICS ELECTRONICS HISTORY HISTORY of SCI & TECH MATH STUDIES LEARN FRENCH STUDY GUIDE PHOTO GALLERY
ATOMIC and NUCLEAR ELECTRICITY and MAGNETISM MEASUREMENTS MECHANICS OPTICS PRACTICAL WORK QUESTIONS RELATIVITY THERMAL PHYSICS WAVES
MECHANICS
Google
Custom Search
Sine of Angle and Angle in Radians
As stated here, the angle θ in radians is defined by considering the arc of a circle
 
A right angled triangle including θ has been added to this diagram of a segment of a circle.  
   
From this, we have  
 
It should be clear from this diagram that these two ratios are not equal (s is noticeably longer than y).  
For example, if θ = 60 then  
 
   
Here the angle is smaller, maybe about 30.  
Now we find  
   
 
 Already quite close...    
   
   
Now consider an even smaller angle (diagram enlarged to be able to put the letters on it!)  
   
It is now clear that y is nearly the same length as s.  
   
   
If this angle is 10 then we now have  
   
 
So, even at 10, the angle is now small enough for these two ratios to be equal, to three decimal places.  
   
N.B.  
Remembering that tanθ is defined as  
 
we could use similar reasoning to find that for small angles tanθ is also equal to θ in radians.  
   
In conclusion, for small angles, (usually considered to mean 3 or less):  
 
SITE MAP
WHAT'S NEW
ABOUT
PRIVACY
COPYRIGHT
SPONSORSHIP
DONATIONS
ADVERTISING
 

© The Open Door Team
2016
Any questions or
problems regarding
this site should be
addressed to
the webmaster

David Hoult 2017

Hosted By
Web Hosting by HostCentric

 
SiteLock
 
 
Mechanics Index Page