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An endeavour to improve the quality of education have been made by improving the implementation of learning. The effort has not been enough to show satisfactory results. This can be seen from the mathematics learning achievement shown by the students still low. Based application PAMER UN 2017 by PUSPENDIK, Mathematics National Exam problems that have the lowest absorption is on trigonometry application. This study aimed to find out the errors of students in solving the HOTS type problem in the application of trigonometry. The type of this research is qualitative descriptive research. The subjects of the research are 189 students from three Vocational High Schools in Gunungkidul Regency, Indonesia, with high, medium and low school category using stratified cluster random sampling technique. To collect the data, this research conducted observations, tests, and interviews. Data analysis techniques include data reduction, triangulation of data that was compared with data result of observation, test, and result of interviews. The results of the analysis show there were three types of errors, namely error type I (understand the meaning of the problem), error type II (applying the concept), and error type III (calculating). The cause of student error type I was lack of understanding the meaning of the problem to make mathematical modeling. In the error type II, students have difficulties distinguishing between V-shaped depression and elevation, students were confused to use the concepts and formulas. Error type III is when the students were not precise in the calculations or in a hurry to do the problem.

Earthquake is the shaking of the earth's surface due to the shift in the earth's plates. This disaster often happens in Indonesia due to the location of the country on the three largest plates in the world and nine small others which meet at an area to form a complex plate arrangement. An earthquake has several impacts which depend on the magnitude and depth. This research was, therefore, conducted to classify earthquake data in Indonesia based on the magnitudes and depths using one of the data mining techniques which is known as clustering through the application of k-medoids and k-means algorithms. However, k-medoids group data into clusters with medoid as the centroid and it involves using clustering large application (CLARA) algorithm while k-means divide data into k clusters where each object belongs to the cluster with the closest average. The results showed the best clustering for earthquake data in Indonesia based on magnitude and depth is the CLARA algorithm and five clusters were found to have total members of 2231, 1359, 914, 2392, and 199 objects for cluster 1 to cluster 5 respectively.