Trigonometry is integral to mathematics education. The field of trigonometry plays a crucial role in the study of mathematics and its applications. Despite the importance of the subject, students struggle to understand trigonometric constructs such as angle measure. It has also been noted how students struggle to understand transformations of functions generally. Our review of the literature found few studies specifically on students’ understanding of transformations of trigonometric functions, but evidence exists showing students have difficulties with the concept. Here, a MATLAB program called TrigReps is discussed. TrigReps accepts four inputs for the algebraic representation (a)sin(bx + c) + d, and provides three additional representations as outputs. Students are presented with a graphical representation, an auditory representation, and a dynamic representation of a radius rotating around a unit circle. TrigReps has potential to be a useful tool for teaching transformations of trigonometric functions. In particular, it may be able to help students justify why combinations of horizontal transformations are counterintuitive. TrigReps is analytically sound in its design: it is interactive, dynamic, and displays Multiple External Representations (MERs) simultaneously. Initial data support its usefulness in a trigonometry classroom, but more research must be conducted to draw firm conclusions.

中文翻译：

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用技术教授三角函数的转换

三角学是数学教育不可或缺的一部分。三角学领域在数学及其应用的研究中起着至关重要的作用。尽管该学科很重要，但学生仍难以理解三角构造，例如角度测量。还已经指出，学生如何努力地大致理解功能的转变。我们对文献的评论发现，很少有研究专门针对学生对三角函数变换的理解，但有证据表明学生对这一概念有困难。在这里，讨论了一个名为TrigReps的MATLAB程序。TrigReps接受代数表示（a）sin（bx + c）+ d的四个输入，并提供三个附加的表示作为输出。向学生展示图形表示，听觉表示，以及围绕单位圆旋转的半径的动态表示。TrigReps有潜力成为教授三角函数转换的有用工具。特别是，它可能能够帮助学生证明水平变换的组合为何违反直觉。TrigReps在设计上具有合理的分析能力：它是交互式的，动态的，并且同时显示多个外部表示（MER）。初始数据支持其在三角学课堂中的有用性，但是必须进行更多的研究才能得出肯定的结论。TrigReps在设计上具有合理的分析能力：它是交互式的，动态的，并且同时显示多个外部表示（MER）。初始数据支持其在三角学课堂中的有用性，但是必须进行更多的研究才能得出肯定的结论。TrigReps在设计上具有合理的分析能力：它是交互式的，动态的，并且同时显示多个外部表示（MER）。初始数据支持其在三角学课堂中的有用性，但是必须进行更多的研究才能得出肯定的结论。