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- IN THIS EXAMPLE WE WANT TO DETERMINE AN ANGLE
BETWEEN 0 AND 360 DEGREES
THAT IS COTERMINAL TO 1,524 DEGREES.
REMEMBER COTERMINAL ANGLES HAVE THE SAME TERMINAL SIDE
IF SKETCHED IN STANDARD POSITION.
SO LET'S GO AHEAD AND SKETCH THIS IN STANDARD POSITION.
THIS IS A POSITIVE ANGLE,
SO WE'LL ROTATE COUNTERCLOCKWISE
FROM THE POSITIVE X-AXIS.
AND SINCE 360 DEGREES REPRESENTS ONE REVOLUTION,
YOU CAN SEE WE'LL HAVE MULTIPLE REVOLUTIONS
FOR 1,524 DEGREES.
SO IF WE ROTATE ONCE AROUND THAT WOULD BE 360 DEGREES.
ANOTHER ROTATION WOULD BE 720 DEGREES,
SO LET'S GO AHEAD AND SEE HOW MUCH MORE WE HAVE TO ROTATE.
IF WE ROTATED TWO REVOLUTIONS ALREADY,
WE CAN SUBTRACT 720 DEGREES FROM 1,524 DEGREES.
WE STILL HAVE TO ROTATE ANOTHER 804 DEGREES.
SO WE CAN SEE IF 720 DEGREES IS TWO REVOLUTIONS.
WE'LL HAVE TO ROTATE TWO MORE TIMES AROUND.
THERE'S ONE MORE, AND THERE'S TWO MORE.
LET'S GO AHEAD AND SUBTRACT ANOTHER 720 DEGREES.
SO WE HAVE TO ROTATE ANOTHER 48 DEGREES
FROM THE POSITIVE X-AXIS.
SO IT'S GOING TO BE SOMEWHERE--
MAYBE SOMEWHERE IN HERE.
AND THAT'S REALLY THE KEY TO ANSWERING THIS QUESTION.
WE KNOW THIS IS THE TERMINAL SIDE TO 1,524 DEGREES,
BUT THE KEY IS WE ROTATED ANOTHER 84 DEGREES
FROM THIS POSITIVE X-AXIS TO REACH 1,524 DEGREES.
SO 84 DEGREES WOULD BE THE MEASURED ANGLE
THAT WE'RE LOOKING FOR THAT'S COTERMINAL TO THE GIVEN ANGLE
BETWEEN 0 AND 360 DEGREES.
AND WE KNOW FROM A PREVIOUS VIDEO,
IN THE MOST GENERAL CASE,
ANY ANGLE THAT'S COTERMINAL TO,
LET'S SAY, THETA WOULD BE THETA + 360 DEGREES x K
WHERE K IS SUM INTEGER.
SO WE COULD DO, IS JUST TAKE OUR ANGLE AT 1,524 DEGREES
AND THEN ADD MULTIPLES OF 360 DEGREES x K
WHERE K IS NEGATIVE TO OBTAIN AN ANGLE
THAT'S BETWEEN 0 AND 360 DEGREES.
AND SINCE WE HAD FOUR COMPLETE REVOLUTIONS,
IF WE LET K = -4 WE'D HAVE 360 DEGREES x -4,
WHICH IS EQUAL TO -1,440,
WHICH WOULD GIVE US A SUM OF 84 DEGREES.
SO FOR ANY VALUE OF K, AS LONG AS K IS AN INTEGER,
WE WOULD HAVE AN ANGLE THAT'S COTERMINAL TO THE GIVEN ANGLE.