Pre-Calc Exam Notes 1

Pre-Calc Exam Notes 1 - 1.1 Angles Recall the following...

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1 Right Triangle Trigonometry Trigonometry is the study of the relations between the sides and angles of triangles. The word “trigonometry” is derived from the Greek words trigono ( τρ ´ ιγων o), meaning “triangle”, and metro ( µǫτρ ´ ω ), meaning “measure”. Though the ancient Greeks, such as Hipparchus and Ptolemy, used trigonometry in their study of astronomy between roughly 150 B.C. - A.D. 200, its history is much older. For example, the Egyptian scribe Ahmes recorded some rudi- mentary trigonometric calculations (concerning ratios of sides of pyramids) in the famous Rhind Papyrus sometime around 1650 B.C. 1 Trigonometry is distinguished from elementary geometry in part by its extensive use of certain functions of angles, known as the trigonometric functions . Before discussing those functions, we will review some basic terminology about angles.
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Unformatted text preview: 1.1 Angles Recall the following de±nitions from elementary geometry: (a) An angle is acute if it is between 0 ◦ and 90 ◦ . (b) An angle is a right angle if it equals 90 ◦ . (c) An angle is obtuse if it is between 90 ◦ and 180 ◦ . (d) An angle is a straight angle if it equals 180 ◦ . (a) acute angle (b) right angle (c) obtuse angle (d) straight angle Figure 1.1.1 Types of angles In elementary geometry, angles are always considered to be positive and not larger than 360 ◦ . For now we will only consider such angles. 2 The following de±nitions will be used throughout the text: 1 Ahmes claimed that he copied the papyrus from a work that may date as far back as 3000 B.C. 2 Later in the text we will discuss negative angles and angles larger than 360 ◦ . 1...
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