The paper focuses on four upper secondary students' collaborative small-group mathematical reasoning (MR) with respect to a sinusoidal function. The students were collaboratively engaged in a process of MR regarding the relationships between mathematical theoretical descriptions of parameters in the algebraic expression of the sinusoidal function and their counterparts when identifying these parameters together with their numerical value in a problem situation. Students' reasoning on the mathematical tool of this sinusoidal function is manifold and multicoloured. Adopting a dialogical approach to the analyses of student interaction, the study reveals that the students' MR, viewed as comprising both process aspects and structural aspects, is characterised by three features. Firstly, the analyses show that the students' MR is characterised by tensions between the mathematical tool and its use in situ, called resistance. Secondly, the students' MR is characterised by their use of semiotic means of objectification such as deictics, gestures, linguistic devices and the text book. Thirdly, the analyses reveal that MR is characterised by the students' efforts to interthink and collaborate in order to achieve the goal of their collective task solving. All four students contributed to the collective MR, however, in various ways and to a varying degree.