Algebra/Trig Review - Pauls Online Math Notes - Lamar University

Algebra/Trig Reviewπ πIn fact can be any of the following angles + 2 π n , n= 0, ± 1, ± 2, ± 3, In this case6 6n is the number of complete revolutions you make around the unit circle starting at 6π .Positive values of n correspond to counter clockwise rotations and negative values of ncorrespond to clockwise rotations.So, why did I only put in the first quadrant? The answer is simple. If you know the firstquadrant then you can get all the other quadrants from the first. You’ll see this in thefollowing examples.Find the exact value of each of the following. In other words, don’t use a calculator.10.⎛2π⎞sin ⎜ ⎟⎝ 3 ⎠ and ⎛ 2π⎞sin ⎜−⎟⎝ 3 ⎠SolutionThe first evaluation here uses the angle 2 π 2ππ. Notice that = π − . So 2 π is33 3 3π 2πfound by rotating up from the negative x-axis. This means that the line for 3 3will be a mirror image of the line for 3π only in the second quadrant. The coordinatesfor 2 π π will be the coordinates for except the x coordinate will be negative.332π2ππLikewise for − we can notice that − =− π + , so this angle can be found by33 3π 2πrotating down from the negative x-axis. This means that the line for − will be3 3a mirror image of the line for 3π only in the third quadrant and the coordinates will bethe same as the coordinates for 3π except both will be negative.Both of these angles along with their coordinates are shown on the following unitcircle.© 2006 Paul Dawkins 48http://tutorial.math.lamar.edu/terms.aspx