Examination of eleventh grade students' basic knowledge about the concepts of radians and degrees, and sine and cosine functions

The subject of trigonometry is taught at the 11th and 12th grade levels in secondary education institutions according to the 2018 curriculum published by the Ministry of National Education. Trigonometry is one of the fundamental topics in mathematics and holds an important place in the curriculum. To understand this subject, it is necessary to have a good grasp of the basic concepts. Therefore, in this research, the fundamental knowledge of secondary school 11th grade students regarding the concepts of radians and degrees, as well as sine and cosine functions, has been examined. The participants of the study consist of a total of 85 students from two different types of high schools located in a district of a province in Central Anatolia. Basic qualitative research design was used to examine the students' definitions of trigonometric concepts. Data was collected using a seven-question open-ended questionnaire prepared by the researcher and validated by expert opinion. This questionnaire includes definitions of degrees and radians, questions regarding their relationship, definitions of sine and cosine functions, and basic questions about these functions. It was determined in the study that students did not fully define degrees and radians correctly. Due to not paying enough attention to the degree symbol, and even rarely using it, they accepted angle measurements given in radians as degrees and performed calculations accordingly. Students perceived one radian as 180⁰, equating radians with π and thinking of 1 radian as equal to 1π. It was observed that they were not aware that one radian corresponds to approximately 57.2⁰. Students experienced difficulties in answering conceptual questions about radians. Weak perceptions about radians have also been identified as reasons for students' conceptual misunderstandings. It was found that students could not accurately find the approximate values of sine and cosine functions, and they experienced difficulties in this regard. It is thought that factors such as struggling with angle reduction, inability to determine the values of well-known angle measurements, and lack of solving similar questions before contribute to this problem.