An angle iscomprised of an initial side and a terminal side connected at thevertex. It looks similar to a hour and minute hand on a clockconnected at the center. The difference is the initial andterminal sides are the same length and the initial side stays inthe same position aiming at 3 o’clock as the terminal sidesrotates around. Counter clockwise rotations are positive andclockwise rotations are negative. When both sides initiallyaim at 3 o’clock, this begins a revolution at zerodegrees. When the terminal side is first rotated counterclockwise to 12 o’clock, this makes a 90 degree angle asmeasured on a protractor. One full rotation counter clockwisefrom 3 o’clock to 3 o’clock referred to as onerevolution is 360 degrees and we can consider multiplerevolutions. Two revolutions is 720 degrees, threerevolutions is 1080 degrees, etc. Clockwise negative anglesare measured similarly. 0, 360, 720, 1080, -360, -720, -1080degrees are co-terminal because they are in the same position, allaim at 3 o’clock. 45, -315, 405 degrees are co-terminalbecause they are in the same position.

As we rotatethe terminal side whichever direction let us consider the arc thatis traced by the tip of its terminal side as it is rotated. An arc that is traced by one revolution is a circle. Wecommonly refer to the length of an arc traced by 360 degrees as thecircumference of a circle. Since the circumference formulaonly measures arc length for 360 degrees, historically a formulawas constructed to measure arc length for any size angle which wasshown in class. Notice arc length depends upon the length ofthe initial and terminal side which is commonly calledradius.

Just like thereis a standard and a metric system of measurement, 1 inch equalsabout 2.5 centimeters, similarly there is an alternativemeasurement to degrees called radians. One degree is about.02 radians and one radian is about 57.3 degrees. Thedefinition of one radian is an angle that traces and arc that has alength equal to the radius.

Project 2:Co-terminal Angles

Instructions:Draw a circle with a compass and label angles starting at 0 zerodegrees that are multiples of 30, 45, 60, 90 degrees for tworevolutions counter clockwise and clockwise using aprotractor.