Christoph Fuhrmann analyzes and tests the application of the trigonometric model, a new item response model. Unlike the Rasch model, which is used in PISA or TIMSS evaluations, the author derives the mathematical properties of the trigonometric model and presents content implications for an extended data analysis made possible by the model based on trigonometric evaluation strategies. He demonstrates that the trigonometric model—while maintaining the specific objectivity characteristic of the Rasch model—exhibits a constant and smaller parameter estimation error. By incorporating information from response patterns, it is capable of identifying misconceptions depending on ability levels, as well as analyzing latent classes and directional data.