A pre-calculus book (Precalculus ed 1 By Miller and Gerken), presents trigonometry in the following order:
2- Trigonometric functions defined on the unit circle
3- Right triangle trigonometry
4- Trigonometric functions of any angle
I do not see the advantage of such a presentation. Topic 2 seems less familiar than 3; and 4 is essentially same as 2. There must be a pedagogical reason for this rearrangement but I do not know what it is.
Some other texts have somewhat similar presentations. In the text by Dugopolski (4 ed) we have 1- Angles, 2- Sine and Cosine on unit circle. In the text by Neal, Gustafson, Hughes we have 1- Angles, 2- Unit circle and trigonometric functions. (That is, no mention of "sine=opposite/hypotenuse" before the unit circle is brought into the picture.)
The order I am familiar with (for example from the text by by Beecher, Penna, Bittinger) goes as follows
B- Right triangle trigonometry
C- Trigonometric functions of any angle (and explain uses of unit circle here)
My question is: Did the shift in order come from research? If so, what is behind it?