Trigonometry

Abstract— The history of trigonometry extends from the beginning of the development of mathematics in Greece to the enlightenment in Europe. While it has evolved from the original chord function to a plethora of functions and identities throughout the ages, many of the identities were already known in antiquity and utilized to measure distance and location in the skies. This paper provides a short review of the development of the sine and a short review of the development of the remaining trigonometric functions. The paper ends with an instructional suggestion to teach the fundamental and Pythagorean trigonometric identities using a diagram composed of the unit circle and similar triangles that will allow high school students to discover the…

Muhammad Al-Khwarizmi to the difference subjects of algebra, geometry and trigonometry. Ideas discovered by Al-Khwarizmi are discussed as well as other concepts that serve as proof of his understanding of various complex ideas we use nowadays. These concepts include simplifying equations, completing the square and trigonometric tables. Key-Words: - Islam, Mathematics, Algebra, Geometry, Trigonometry 1 Introduction Throughout time, cultures and societies have created and discovered amazing…

Pythagoras and Progression Our world is composed of numbers; whether it is formulas or simple math, we are encompassed by a subject that has no beginning or end; it is infinite; the number line goes on forever. The development of these concepts to facilitate our life in a mathematical aspect has been made by several people; moreover, their notions have fulfilled their purpose. Pythagoras of Samos was born in 570 B.C. in Samos, Greece; however, he moved to Egypt, where he lived twenty-two years.…

Trigonometry is otherwise know as the study of relationships between lengths and angles of triangles. Forensic scientists use that part of math in connection with murders; especially blood. By construction right triangles between the wound of the victim (where the blood comes from) and the blood splatters. In most crime scenes knowledge about things like: - Where did the murderer stand? - Where was the victim located? - In which angle did the murder weapon (e. g. dagger) hit the victim? These…

the watermelon. And of course, the best part was at the end, when we all have to eat the watermelon! It was a best memory that I remember as one the fun way of learning. I feel as if math skills are not at full potential, because sometimes I will not understand strategies, and often cannot even remember formulas because of how long some are. For example, sometimes I get area, and volume formulas mixed up with each other. The worst memory of math I had was in middle school when I was in Grade 7.…

Copernicus called the secant the hypotenusa and Viete knew of the equivalence of the ratio of cosecant and secant with cotangent as the reciprocal of tangent, as well as the equivalence of the reciprocal of cosecant with the ratio of cosine and tangent and its equivalence with sine [2]. Oughtred used se arc and sec co arc while Wallis used s and σ and Cavalieri used Se and Se.2. sec written above the angle was used by Albert Girard. Pitiscus in 1595 first used the term trigonometry in the title…

Inverse Functions of Trigonometric Functions As high schoolers go their their teenage years of high school they learn from a variety of subjects. From math to science to history, there is a depth of knowledge to be learned. For math 3 and math 4, we are introduced to the world of trigonometry. So far, we have learned that there are currently three main trigonometric functions, cosine, sine, and tangent. But today I want to explore the other side of the trigonometric world, the inverse…

Sitting in Algebra II, you may think to yourself: when am I ever going to use any of this in the real world? You are going to use all of the skills you learn in Algebra II more than you will ever realize. Using trigonometry, linear functions, series and sequences, and rational functions are prevalent in everyday life. In this fun, exciting report, you will learn about many situations in which you use Algebra II without even recognizing it! Trigonometry is a widely used math concept in everyday…

Our society is defined, partially, by the concern to capture memories within physical keepsakes in attempt to remember the accomplishments we strived for and the failures we drag begrudgingly behind our individual egos. At times, during this lifetime process, we often take universal knowledge, whether taught, told, or thrived upon, to aid us in our journey. And through this we personalize said knowledge to fit our needs. In turn, this provides us with necessary meaning and purpose. However,…

In this lab we will explain how to deduce the equation landing position of the ball thrown by the robotic arm stand. We must create the equations in terms of the radius, height, arm rotation speed, and release angle. The equations must be made with those variables because, those variables are what can change where the ball will land in the cup, and will make the equation more useful to the client. To make sure the equation will remain accurate we have to keep track of all the units throughout…