7-4 refernce angles

today i am going to show you how to find a reference angle. the number one thing you should know about refernce angles is they are like reduced fractions. they have to be between 0 degrees and 90 degrees. there are 3 steps that should be followed when finding a refernce angle. 1) find the orginal quadrant and sketch. 2) determine if the angle is positve or negative using the unit circle. 3) subtract 360 dgrees or 180 degrees until the |theta| is between 0 degrees and 90 degrees. this will all make sense in the examples below.


EX: find a refernce angle
a) sin 128 degrees              b ) cos 128 degrees         c) sin(-37 degrees)          d) cos 500 degrees
1) 2nd quadrant. b/w          1) 2nd quadrant.b/w        1) 4th quadrant. b/w        1) 2nd quadrant. b/w 90 and
90 and 180.                           90 and 180.                  270 and 360.                 180 bc 500-360 is 140.
2) postive. y/r which            2) negative. x/r which       2) negative. y/r which      2) negative. x/r which
= +/1                                   = -/1                               = -/1                               =-/1
3) 128-180=|-52|                3) 128-180=|-52|            3) -37 is already b/w       3) 500-360-180=|-40|
 52                                       52                                      0 and 90=|-37| = 37     40
refernce angle is sin 52         refernce angle is -cos 52    refrence angle is -sin 37   refernce angle is -cos 40