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Converting Between Degrees and Radians 1356 Views


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Description:

If you bake a pie that's 360 degrees...you should probably let it cool down a little. While you're waiting to ingest all those delicious, delicious calories, though, watch this video.

Language:
English Language

Transcript

00:03

converting between degrees and radians a la shmoop

00:07

the citizens of Krusty hollow have just finished making the world's largest [Women holding large apple pie]

00:12

apple pie unfortunately for them the tempting aroma has attracted the

00:16

attention of a handful of giants living on a cloud above them

00:20

Tommy, Teddy, Benny, Manny, Gary and Jenny the Giants show up to crash the party [Giants appear]

00:25

and crusty hollow-ites scatter.... to divide the pie evenly Tommy pulls out

00:31

his handy-dandy protractor which measures angles in degrees we know that

00:36

a circle is 360 degrees if Tommy evenly divides that between he and his five [Circle divided into 5 portions]

00:42

friends then each giant gets 1/6 of 360 or 60 degrees of pie... because Giants are

00:49

always challenging themselves Tommy wonders if he can convert the

00:53

number of degrees in his slice to radians back in giant-high, Tommy learned

00:57

that a full circle has two pi radians which is equal to 360 degrees so to

01:03

convert from degrees to radians all he has to do is multiply the number of [Conversion of degrees to radians appears]

01:06

degrees by pi over 180 remember Tommy slice is 60 degrees so 60 times pi over

01:13

180 simplified is the same thing as pi over 3 after gorging themselves on pi 2

01:20

of the giants head back into the cloud but right after they leave the remaining [Two giants hop onto cloud and disappear]

01:24

Giants discover a second massive pie in the neighboring town of compote hills...

01:29

Tommy cuts the pie into 4 even slices each with a measure of pi over 2 radians

01:35

then wonders what that would be in degrees well if the number of degrees [Pie divided into 4 sections]

01:42

multiplied by pi over 180 gives you the number of radians then what if we flip

01:46

the fraction around to get from radians to degrees the formula that Tommy uses

01:51

to convert from radians to degrees is the number of radians multiplied by 180

01:55

over pi equals number of degrees... so in the equation pi over 2

02:00

times 180 over pi the pi in the numerator and the pi in the denominator

02:04

cancel out and 180 divided by 2 gives you 90 degrees each slice of pie is pi

02:10

over 2 radians or 90 degrees there you go Tommy feels quite satisfied both by [Tommy and giants stood together]

02:16

the desert and his formidable algebra skills

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