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Very basic trigonometry question?

  1. Jul 19, 2011 #1
    1. The problem statement, all variables and given/known data

    Well basically i'm trying to learn trigonometry from a textbook. It shows a rule,
    to change from degrees to radians, multiply by pi/180.
    to change from radians to degrees, multiply by 180/pi .


    2. Relevant equations



    3. The attempt at a solution
    I'm the type of person that wants to know why what works. I cannot sleep when i cannot understand the background work of an rule. why do those rules work? ty
     
  2. jcsd
  3. Jul 19, 2011 #2

    Dick

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    It's because a full circle is 2*pi radians and it's also 360 degrees. So (2*pi radians)=(360 degrees). So (dividing both sides by 2*pi), 1 radian=(360/(2*pi)*degree=(180/pi)*degree. That's your first conversion, you do the second.
     
  4. Jul 19, 2011 #3

    phinds

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    Dick's response is correct, but a more fundamental answer is that it is inherent in the definition of degrees and radians. They are just different units for the same thing, like miles and kilometers.
     
  5. Jul 20, 2011 #4

    ehild

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    The length of an arc s in a circle belonging to the central angle φ is s=(φ(degree)/360°) (2Rπ). Instead of degrees, we can measure the angle with the ratio of (arc length / radius): φ(radian)=s/R. Comparing with the previous equation φ(radian)=s/R=2π ( φ(degrees)/360°).

    ehild
     
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