Trigonometrik Fonksiyonların Toplam ve Fark Formüllerinin Ortaöğretim Düzeyinde Görselleştirilmesi

Öz

İspat matematikçilerce, matematik alanının ve uygulamasının temeli olarak görülür. Birçok öğrenci ise niçin ispat yapmayı öğrenmek zorunda olduklarına anlam verememektedir. Trigonometri ortaöğretim matematik müfredatının önemli bir konusudur. Trigonometriyle çalışırken öğrencilerin çoğu eşitlikleri ezberlemekte ve bunları rutin alıştırmaları çözmek için uygulamaktadırlar. Öğrencilerden trigonometride ispat yapmaları istendiğinde, eşitlikleri taraf tarafa toplamaya dayalı cebirsel dönüşümler yapmaktadırlar. Trigonometri kavramlarını öğrencilerin daha iyi anlamalarını sağlamak için görsel ispatlar yararlı olabilir. Bu çalışmada toplam ve fark formüllerinin görsel şekillerle ispat edilmesi ve bunların diğer araştırmacılara tanıtılması amaçlanmıştır. Bu amaçla görsel ispat ve cebirsel ispat sırasıyla yapılmış ve bunlarla ilgili bazı öneriler verilmiştir.

Anahtar Kelimeler

• Görselleştirme, toplam ve fark formülleri, görsel ispat, cebirsel ispat

Abstract

Proof is viewed by mathematicians as central to the discipline and practice of mathematics. Most students are unable to understand why they must learn how to write a proof. Trigonometry is an important subject in the secondary school mathematics curriculum. When studying trigonometry, most students just have to memorize a set of identities and to apply them to solve routine exercises. When students are asked to do proofs in trigonometry, they do some proofs usually consist of algebraic transformations linking a side of an identity to the other side. To promote students' understanding of trigonometric concepts, visual proofs may be beneficial. In this study, it is aimed to prove the sum and difference formulas in trigonometry by visual figures and to introduce them to other researchers. For this goal, visual proof and algebraic proof processes were made respectively and some suggestions were given about them

Keywords

• Visualization, sum and difference formulas, visual proof, algebraic proof

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