degree to radians with nonspecial points?

[IllWill]

im having problems converting numbers that arent special points on the unit circle to radians. i think i have it right but im not positive. this isnt an actual problem in my book, but here is an example i made up similar to the ones we are working on:

convert 336 degrees to radians.

here is what i think im suppose to do:

336/1 * pi radians/180 = 336 pi radians/180 = 28 pi radians/15.

 

[soroban]

Hello, IllWill!

Convert 336 degrees to radians.

Here is what i think im suppose to do:

336/1 * pi radians/180 = 336 pi radians/180 = 28 pi radians/15.

Absolutely correct!

Do you understand the underlying principle?

We know that: . 180 degrees .= .π radians

. . . . . . . . . . . . . . . . 180 deg . . . . . . π rad
We form fractions: . ----------- . or . -----------
. . . . . . . . . . . . . . . . . π rad . . . . . . 180 deg

To convert an angle, we select the <u>correct</u> fraction to multiply by.


For your problem:

. . . 336 deg . . π rad . . . . . 28 π
. . . ---------- . ---------- . = . ------- radians
. . . . . .1 . . . .180 deg . . . . .15

Of course, we reduce the fractions as much as possible,
. . but note that the "degrees" cancel and the answer is in "radians".
And that is how we select the proper fraction.

 

[Guest]

Right. It isn't really a conversion between units, though. "1 radian" is just the number 1. "1 degree" is the number pi / 180.

336^o
= 336 * 1^o
= 336 * (pi / 180)
= 28pi / 15

The word "radian" just exists to describe a system of unitless angle measurement.

 

[IllWill]

thanks. i just wanted to clear that up and make sure i had the right idea.