# Examples: Converting Angles in Degree Measure to Radian Measure

– LET’S TAKE A LOOK AT SEVERAL
EXAMPLES OF CONVERTING AN ANGLE IN DEGREE
MEASURE TO RADIAN MEASURE. AND TO DO THIS CONVERSION
WE’RE GOING TO MULTIPLY IT BY A UNIT FRACTION. LET’S DISCUSS BRIEFLY WHERE
THAT UNIT FRACTION COMES FROM. 2/PI RADIANS IS EQUAL
TO 360 DEGREES. SO IF WE TAKE THIS EQUATION
AND DIVIDE BOTH SIDES BY 360 DEGREES,
AS WE SEE HERE ON THE LEFT, AND THEN SIMPLIFY WE WOULD HAVE
PI/180 DEGREES IS EQUAL TO 1. THIS IS A UNIT FRACTION. BUT WE COULD HAVE ALSO DIVIDED
BOTH SIDES OF THE EQUATION BY 2/PI RADIANS
AS WE SEE HERE ON THE RIGHT. AND IF WE DID THAT WE’D HAVE THE
UNIT FRACTION 180 DEGREES/PI. TO HELP DETERMINE
WHICH UNIT FRACTION TO USE TO DO THE CONVERSION IT
HELPS TO THINK OF 135 DEGREES AT A FRACTION. SO WE’LL PUT IT OVER 1 AND WE KNOW IF WE WANT
TO CONVERT DEGREES TO RADIANS WE NEED TO SIMPLIFY
OUT THE DEGREE MEASURE. AND WE CAN DO THAT IF THE DEGREE
MEASURE IS IN THE DENOMINATOR. SO WE’LL USE THIS UNIT FRACTION TO CONVERT
FROM DEGREES TO RADIANS. AND WE’LL USE THIS UNIT FRACTION
IN ANOTHER VIDEO TO CONVERT
FROM RADIANS TO DEGREES. SO WE’RE GOING TO MULTIPLY
ALL OF THESE BY PI/180 DEGREES. AND THEN WE’LL SIMPLIFY
AND THEN WE’LL MULTIPLY. 135 AND 180 HAVE A COMMON FACTOR
OF 45. THERE ARE 3 FORTY-FIVES IN 135 AND THERE ARE 4 FORTY-FIVES
IN 180. AND THE UNITIES OF DEGREES
ALSO SIMPLIFY OUT. SO WE’RE LEFT WITH 3PI
DIVIDED BY 4 RADIANS AND WE’RE GOING TO DO
THE REST OF THESE THE SAME WAY. WHERE IT IS A FRACTION MULTIPLY
IT BY PI DIVIDED BY 180 DEGREES. HERE WE HAVE A COMMON FACTOR
OF 60. THERE’S 1 SIXTY IN SIXTY
THAT SIMPLIFIES TO A -1. THERE ARE 3 SIXTIES IN 180. AND THEN AGAIN THE DEGREES
SIMPLIFY OUT. SO WE’RE LEFT
WITH -1PI DIVIDED BY 3 OR JUST -3PI
DIVIDED BY 3 RADIANS. PUT THE 15/1,
MULTIPLY BY PI/180 DEGREES. HERE WE HAVE A COMMON FACTOR
OF 15 SO THIS SIMPLIFIES TO 1 AND THERE ARE 12 FIFTEENS
IN 180. SO WE HAVE 1PI DIVIDED BY 12 OR
JUST PI DIVIDED BY 12 RADIANS. AND WE’LL TAKE A LOOK
AT ONE MORE. 48 AND 180 HAVE A COMMON FACTOR
OF 12. THERE ARE 4 TWELVES’
IN 48 SO THIS SIMPLIFIES TO -4. AND THERE ARE 15 TWELVES’
IN 180. SO HERE WE HAVE -4PI
DIVIDED BY 15 RADIANS.

#### 3 Comments

• Bryce Norwood says:

OMG… thank you so much, you dont get nearly enough credit!

• Joe Rocks says:

How about you do harder problems, instead of the simple math you could do this in your hear. like -196 or something. Because on test, it's not going to be as simple as pie over 4. And just because the two numbers have a common denominator it means you can just cancel everything out?

• Joe Rocks says:

or like -450.