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- WELCOME TO AN EXAMPLE OF DETERMINING A POSITIVE
AND NEGATIVE COTERMINAL ANGLE TO A GIVEN ANGLE IN RADIANS
RATHER THAN DEGREES.
LET'S GO AHEAD AND SKETCH THIS ANGLE IN A STANDARD POSITION.
HERE IS THE INITIAL SIDE.
IF YOU'RE STILL NOT COMFORTABLE WITH RADIANS
YOU COULD CONVERT IT TO DEGREES.
BUT HOPEFULLY BY NOW YOU RECOGNIZE THIS AT 60 DEGREES.
SO PI/3 RADIANS IS APPROXIMATELY HERE.
AND IF WE WANT ANOTHER COTERMINAL ANGLE,
MEANING AN ANGLE THAT HAS THE SAME TERMINAL SIDE,
WE JUST NEED TO ADD OR SUBTRACT MULTIPLES OF 2/PI RADIANS
TO THE GIVEN ANGLE IN RADIANS.
SO WE'RE GOING TO BE ADDING OR SUBTRACTING MULTIPLES OF 2/PI
TO PI/3 LET'S GO AHEAD AND WRITE 2PI/1 WITH A DENOMINATOR OF 3
SO WE CAN EASILY ADD IT TO PI/3 RADIANS.
SO WE'D HAVE TO MULTIPLE THE NUMERATOR AND DENOMINATOR BY 3.
SO 2/PI RADIANS IS EQUAL TO 6PI/3 RADIANS.
SO DETERMINE ANOTHER POSITIVE COTERMINAL ANGLE TO PI/3 RADIANS
WE'LL JUST TAKE PI/3 RADIANS AND ADD 2/PI
OR IN THIS CASE 6PI/3 RADIANS.
WELL, PI/3 IS THE SAME AS 1PI/3.
SO ANOTHER POSITIVE COTERMINAL ANGLE WOULD BE 7PI/3 RADIANS
AND THAT WOULD BE THIS ANGLE HERE.
AND TO DETERMINE A NEGATIVE COTERMINAL ANGLE
WHAT WE'LL DO IS SUBTRACT 2/PI RADIANS OR 6PI/3 RADIANS
SO WE'LL HAVE PI/3 OR 1PI/3 - 6PI/3 RADIANS
AND THIS WILL EQUAL -5PI/3 RADIANS.
AND THIS WOULD BE THE COTERMINAL ANGLE
THAT ROTATES CLOCKWISE HERE.
SO IN GENERAL TO DETERMINE A COTERMINAL ANGLE
TO AN ANGLE IN RADIANS
WE WOULD TAKE THE GIVEN ANGLE FADA
AND ADD MULTIPLES OF 2/PI x (K) WHERE (K) IS SOME INTEGER.
SO IF (K) IS POSITIVE WE WOULD ADD MULTIPLES OF 2/PI.
AND IF (K) WAS NEGATIVE IT WOULD BE THE SAME AS SUBTRACTING
MULTIPLES OF 2/PI RADIANS.
LET'S TAKE A LOOK AT ONE MORE EXAMPLE.
AGAIN, THE ANGLE IS GIVEN IN RADIANS
BUT THIS TIME IT'S A NEGATIVE ANGLE.
SO THE GIVEN ANGLE WILL ROTATE CLOCKWISE 4PI/5 RADIANS.
AND IF YOU HAVE A HARD TIME FIGURING OUT
WHAT ANGLE THIS ONE.
WE KNOW THAT HALF OF REVOLUTION CLOCKWISE WOULD BE -PI RADIANS.
SO WE'LL ROTATE 4/5 OF HALF A REVOLUTION CLOCKWISE
SO MAYBE SOMEWHERE IN HERE.
THIS WOULD BE OUR GIVEN ANGLE.
AND, AGAIN, BECAUSE WE HAVE TO ADD OR SUBTRACT
MULTIPLES OF 2/PI RADIANS
LET'S GO AHEAD AND CONVERT 2PI/1 TO A DENOMINATOR OF 5.
SO MULTIPLE BOTH THE NUMERATOR AND DENOMINATOR BY 5.
2/PI RADIANS IS THE SAME AT 10PI/5 RADIANS.
SO FROM WHERE WE CAN TAKE OUR GIVEN ANGLE -4PI/5
AND ADD 10PI/5 RADIANS.
THAT WILL GIVE US 6PI/5 RADIANS
AND THAT WOULD BE THIS ANGLE HERE.
NOW TO FIND ANOTHER NEGATIVE COTERMINAL ANGLE
WE'LL GO AHEAD AND SUBTRACT 10PI/5 RADIANS.
AND THAT WOULD BE -14PI/5 RADIANS.
AND FOR THIS ANGLE WE'D ROTATE CLOCKWISE
ONE COMPLETE REVOLUTION
AND THEN BACK TO THE SAME TERMINAL SIDE.