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Advisor(s)
Abstract(s)
Este trabalho encontra-se dividido em duas partes: pesquisa científica e prática de ensino supervisionada.
No trabalho científico fez-se uma investigação sobre os povos que contribuíram para a descoberta
e evolução da trigonometria. Recorda-se a terminologia, o conceito de círculo trigonométrico e a
transição das razões trigonométricas para as funções trigonométricas. Com o desenvolvimento da
trigonometria surgiram identidades trigonométricas fundamentais neste ramo da matemática, e que
hoje são imprescindíveis em várias outras áreas. Identidades que serão enunciadas e demonstradas
neste trabalho, nomeadamente, o teorema de Ptolomeu, fórmula fundamental da trigonometria,
fórmulas do seno e cosseno da soma e da diferença, lei dos senos e dos cossenos. É feita uma contextualização
do ensino da trigonometria no ensino básico e secundário e são ainda apresentados
dois exemplos da aplicabilidade da trigonometria que foram objeto de pesquisa nas disciplinas de
Seminário de Investigação Matemática. A encerrar esta parte é feita uma análise de uma nova
abordagem sobre a trigonometria, chamada de Trigonometria Racional.
Relativamente à prática de ensino supervisionada é feita uma descrição sumária do que foi realizado
no estágio pedagógico. É apresentado um conjunto de 6 planificações que correspondem a
aulas lecionadas, no 9º e 12º ano de escolaridade.
This project is divided into two parts, the scientific research and the supervised teaching practice. The scientific research part started with a short list of the historical contributions to the discovery and evolution of trigonometry, recalling the terminology, the concept of trigonometric circle and the transition of trigonometric ratios to trigonometric functions. With the development of trigonometry, many fundamental trigonometric identities emerged in this field of mathematics, being essential in many other areas. These identities will be stated and demonstrated in this project, including the Ptolemy method, the trigonometric fundamental formula, the sum and subtraction formulas and the sine and cosine law. A contextualization of trigonometry teaching in Junior High and High Schools is also presented, along with two examples of the applicability of trigonometry which were object of research throughout the subjects of a Seminar on Mathematical Research. Concluding this part, a brief analysis of a new approach on trigonometry, called Rational Trigonometry, is done, too. Regarding the supervised teaching practice, a brief description of what was performed during pedagogical training is produced, presenting a set of 6 lesson plans which correspond to lessons taught in the 9th and 12th grades.
This project is divided into two parts, the scientific research and the supervised teaching practice. The scientific research part started with a short list of the historical contributions to the discovery and evolution of trigonometry, recalling the terminology, the concept of trigonometric circle and the transition of trigonometric ratios to trigonometric functions. With the development of trigonometry, many fundamental trigonometric identities emerged in this field of mathematics, being essential in many other areas. These identities will be stated and demonstrated in this project, including the Ptolemy method, the trigonometric fundamental formula, the sum and subtraction formulas and the sine and cosine law. A contextualization of trigonometry teaching in Junior High and High Schools is also presented, along with two examples of the applicability of trigonometry which were object of research throughout the subjects of a Seminar on Mathematical Research. Concluding this part, a brief analysis of a new approach on trigonometry, called Rational Trigonometry, is done, too. Regarding the supervised teaching practice, a brief description of what was performed during pedagogical training is produced, presenting a set of 6 lesson plans which correspond to lessons taught in the 9th and 12th grades.
Description
Keywords
Círculo Trigonométrico Lei dos Cossenos Lei dos Senos Teorema de Ptolomeu Triângulo Retângulo Trigonometria Trigonometria Racional