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Because it is also used at university level in fields such as physics and geodesy, an assessment of students’ prior knowledge is important before starting courses. The study develops a multiple-choice test covering triangle and circle trigonometry concepts, then verifies content validity with three experts and performs item analysis with 58 first-year students.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/construction-and-analysis-of-test-in-triangle-and-circle-trigonometry-research-article/577529/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/construction-and-analysis-of-test-in-triangle-and-circle-trigonometry-research-article/577529.png","ImageObject",300,407,{"name":92,"@type":93},"Lucas Martin","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-31","2026-10-15",true,{"@type":102,"interactionType":103,"userInteractionCount":81},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What was the goal of the study?","Question",{"text":112,"@type":113},"To develop a test that checks students’ achievements in triangle trigonometry and the basics of circle trigonometry, and to assess prior knowledge before university courses.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How was the test content validated?",{"text":117,"@type":113},"Three experts evaluated the test content validity; a corrected version was then prepared for student administration.",{"name":119,"@type":110,"acceptedAnswer":120},"Who took the test and what was done afterward?",{"text":121,"@type":113},"The corrected test was given to 58 first-year students, followed by test and item analysis to produce a final version usable as an initial prior-knowledge test.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},577529,1792667717,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":81,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":44,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":144,"preview_page_count":4},8796095360427,"https://ap-avatar.wpscdn.com/davatar_994ba38a5ba835b3df7d355c54d3ed8d","International Electronic Journal of Mathematics Education  \n2025, 20(1), em0805 e-ISSN: 1306-3030  \n[https://www.iejme.com](https://www.iejme.com Research Article)[ Research Article](https://www.iejme.com Research Article)  \nOPEN ACCESS  \n\n| Construction and analysis of test in triangle and circle trigonometry\u003Cbr>Dina Kamber Hamzić 1*  , Mirsad Trumić 2  , Ismar Hadžalić 1 \u003Cbr>1 Faculty of Science, University of Sarajevo, Sarajevo, BOSNIA AND HERZEGOVINA\u003Cbr>2 Agricultural and Medical School, Brčko District, BOSNIA AND HERZEGOVINA\u003Cbr>*[Corresponding Author:](Corresponding Author: dinakamber@pmf.unsa.ba)[ dinakamber@pmf.unsa.ba](Corresponding Author: dinakamber@pmf.unsa.ba)\u003Cbr>Citation: Kamber Hamzić, D., Trumić, M., & Hadžalić, I. (2025) . Construction and analysis of test in triangle and circle trigonometry. International\u003Cbr>Electronic Journal of Mathematics Education, 20(1), em0805. [https://doi.org/10.29333/iejme/15734](https://doi.org/10.29333/iejme/15734) |  |\n| --- | --- |\n| ARTICLE INFO\u003Cbr>Received: 22 May 2024\u003Cbr>Accepted: 29 Nov. 2024 | ABSTRACT\u003Cbr>Trigonometry is an important part of secondary school mathematics, but it is usually challenging for students to understand and learn. Since trigonometry is learned and used at a university level in many fields, like physics or geodesy, it is important to have an insight into students ’ trigonometry knowledge before the beginning of the university courses. This research aimed to develop a test in triangle and circle trigonometry, which can be used to test students’ prior knowledge of basic trigonometric concepts. A test with multiple-choice questions was developed based on content and learning outcomes from the secondary school curriculum. After a group of three experts evaluated the content validity of the test, the corrected version was given to 58 first-year students at the Department of Mathematics and Computer Science. After the test and item analysis, a final version of the test was made which can be used as a short initial test to measure students ’ prior knowledge of trigonometry at the beginning of a university course.\u003Cbr>Keywords: circle trigonometry, reliability, triangle trigonometry, validity |\n\nINTRODUCTION  \nTrigonometry is an important area of mathematics. It is used in astronomy, physics, architecture and construction, geodesy, forensics, acoustics, etc. Trigonometry is an indispensable part of secondary school and university mathematics, and as a field that connects geometry, algebra, and graphics, it is an important introduction to differential and integral calculus (Weber, 2008) .  \nUsually, students first learn about trigonometric functions as ratios of side lengths in a right-angled triangle. This approach is good in geometry problems where unknown sides or angles are searched for, but if one needs to determine the value of a trigonometric function for some argument, determine whether it increases or decreases at some interval, draw a graph of the function–this approach does not help (Weber, 2008) . To answer these questions, students have to understand trigonometric functions as functions, not as side length ratios. To define trigonometric functions for arbitrary real numbers, we define trigonometric functions using a unit circle.  \nChin and Tall (2012) introduce three contexts of understanding trigonometry: triangle trigonometry (includes problems connected with the relations of sides and angles in a right-angled triangle), circle trigonometry (includes angles of any size with a vertex at the center of the circle, and properties of trigonometric functions), and analytic trigonometry (includes trigonometric functions expressed with Taylor series and the use of complex numbers to connect exponential and trigonometric functions) .  \nIn the Bosnia and Herzegovina educational system, the study of trigonometry begins in secondary school. Regardless of the school choice (vocational, technical, or grammar school), all students encounter triangle trigonometry ","cbCaih9Ydhvcg8WE","https://ap.wps.com/l/cbCaih9Ydhvcg8WE","pdf",240211,"English","# Abstract\n# Introduction\n## Purpose and educational context\n## Trigonometry understanding contexts\n## Standards and learning outcomes\n# Test construction and analysis","[{\"question\":\"What was the goal of the study?\",\"answer\":\"To develop a test that checks students’ achievements in triangle trigonometry and the basics of circle trigonometry, and to assess prior knowledge before university courses.\"},{\"question\":\"How was the test content validated?\",\"answer\":\"Three experts evaluated the test content validity; a corrected version was then prepared for student administration.\"},{\"question\":\"Who took the test and what was done afterward?\",\"answer\":\"The corrected test was given to 58 first-year students, followed by test and item analysis to produce a final version usable as an initial prior-knowledge test.\"}]","Construction and analysis of test in triangle and circle trigonometry - Research Article | PDF",1792031904,23]