### Exploration of high school students' reasoning in solving trigonometric function problems

#### Abstract

Reasoning has been extensively studied by many experts. However, Research on student reasoning in trigonometric problem solving, particularly those related to logical thinking skills is still sorely needed. This study aimed to explore students' reasoning in solving trigonometric function problems regarding logical thinking skills. The research was conducted using a qualitative approach. The research subjects involved high school students in Palopo, Indonesia. Based on the logical ability test results, three subjects were selected, namely students with high, medium, and low logical abilities. Research instruments in mathematical problem-solving tasks and interview guidelines are valid and reliable. Data collection was carried out through task-based interviews and think-aloud. The results of the study: (1) the reasoning subjects with high and moderate logical abilities in solving trigonometric function problems are the same in every type of question, always starting with inductive reasoning and then doing deductive reasoning (2) the reasoning of subjects with high and medium logical abilities is different in solving trigonometric function problems in the initial identification. Subjects with low logical ability showed no mental activity in solving trigonometric function problems. The research finding is that the subject has a high logical ability and is solving trigonometric function problems first by inductive reasoning and then deductive reasoning. In general, it is concluded that students with high and moderate logical abilities use inductive and deductive thinking patterns interchangeably in solving trigonometric function problems.

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DOI: https://doi.org/10.24042/ajpm.v13i2.12972

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