title: Constructing and deriving reciprocal trigonometric relations: a functional analytic approach.
abstract: Participants were pretrained and tested on mutually entailed trigonometric relations and combinatorially entailed relations as they pertained to positive and negative forms of sine, cosine, secant, and cosecant. Experiment 1 focused on training and testing transformations of these mathematical functions in terms of amplitude and frequency followed by tests of novel relations. Experiment 2 addressed training in accordance with frames of coordination (same as) and frames of opposition (reciprocal of) followed by more tests of novel relations. All assessments of derived and novel formula-to-graph relations, including reciprocal functions with diversified amplitude and frequency transformations, indicated that all 4 participants demonstrated substantial improvement in their ability to identify increasingly complex trigonometric formula-to-graph relations pertaining to same as and reciprocal of to establish mathematically complex repertoires.
authors: School and Behavioral Psychology, Stephen F. Austin State University, Nacogdoches, Texas 75962, USA. cninness@titan.sfasu.edu
authors: Chris
authors: C
authors: Ninness
authors: Mark
authors: M
authors: Dixon
authors: Dermot
authors: D
authors: Barnes-Holmes
authors: Ruth Anne
authors: RA
authors: Rehfeldt
authors: Robin
authors: R
authors: Rumph
authors: Glen
authors: G
authors: McCuller
authors: James
authors: J
authors: Holland
authors: Ronald
authors: R
authors: Smith
authors: Sharon K
authors: SK
authors: Ninness
authors: Jennifer
authors: J
authors: McGinty
mesh_terms: D000328:Adult; D003196:Computer Graphics; D003194:Computer-Assisted Instruction; D005260:Female; D006801:Humans; D008433:Mathematics / Q000193:education*; D011214:Practice, Psychological