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April 26th, 2009, 02:37 PM   #1
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Converting Vice Versa from Radian to Degrees

I know I've been posting a lot of topics but I found this site to be really helpful. I really want to understand the material and I'm never satisfied until the light bulb turns on.

My question for radian is this,

180degrees = (pi)radian

1.) 1degree = (pi/180)rad

2.) (180/pi) = 1 rad

I get the first one where (pi)radian is half a circle and if you divide half a circle by 180 you get 1 degree.

Now the second on has me stumped. You take 180 degrees and divide it by pi which gives you 1 radian. How does that come to be? What is going on in the second equation? Are you dividing 3.14 into 180 degrees. So basically your trying to find out how many 3.14 fits in 180 degrees? But how is the result equal to 1 radian?
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April 26th, 2009, 03:04 PM   #2
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Re: Converting Vice Versa from Radian to Degrees

Quote:
Originally Posted by David_Lete

180degrees = (pi)radian

1.) 1degree = (pi/180)rad

2.) (180/pi) = 1 rad

I get the first one where (pi)radian is half a circle and if you divide half a circle by 180 you get 1 degree.

Now the second on has me stumped.
Why? Simply divide both sides of a relation by any same quantity, and the relation is still true. So, divide both sides by 180 for the first, and divide both sides by Pi to get the second.
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April 26th, 2009, 03:20 PM   #3
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Re: Converting Vice Versa from Radian to Degrees

I understand that part, but I'm still not understanding it. Or better said I can't visualize it or see how it applies to a half circle. I don't understand it in this sense, if I wasn't taking trigonometry and I was presented with these equations I would be able to solve them easily using algebra. But what does that help me if I don't understand how it applies. Like the first one I understand that (pi)radian is a half circle and if you divide that half circle into 180 sections then you get degrees. So the first one is vividly clear and I understand how it applies but not the same for the second one.
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April 26th, 2009, 03:32 PM   #4
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Re: Converting Vice Versa from Radian to Degrees

Oh, maybe I do understand. For the second one you take 180degrees which is half a circle. Now for radians a half circle contains 3.14. So in this half circle the first, second, and third radians its 57.3degrees, and finally for the last partial radian it's 57.3 * .14 = 8.022.

57.3 * 3 =171.9
57.3 * .14 = 8.022
-------------179.922<------ that's pretty darn close to a half circle. I get it now!!!!! How awesome is that.
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