One of the most confusing topics to students when teaching trigonometry is the concept of reference angles and triangles. Many books do not tie this concept holistically so that students can understand how to compute the reference angle of any angle and also to come up with the reference triangle for that angle.
This e-book will give both the teachers and the students the exact ideas that must be used to compute the reference angle of any angle. The first part of this e-book shows how to label the reference angle of any angle between 0 degrees and 360 degrees. It also shows how to compute the reference angle of any of these angles.
The e-book goes further to show how to compute the reference angle of any angle greater than 360 degrees or less than 0 degrees by tying together the concept of coterminals and reference angles. This flow of ideas seem to miss in all the trigonometry books out there today!
The e-book also show clearly how a student should find any of the six trigonometric ratios for these angles. The ratio must be computed in such a way that the student must pay attention to the the signs of x and y in each of the four quadrants. The computation shows that computing the trigonometric ratio of each angle in each quadrant is equivalent to computing the trigonometric ratio of the acute angle of the reference triangle. The student must remember to factor in the signs in each quadrant appropriately.