# 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.

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

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?

or like -450.