Mathematics for Business, Science, and Technology with MATLAB and Excel Computations, Third Edition

Chapter 4: Fundamentals of Plane Trigonometry

This chapter discusses the basics of trigonometry. It is intended for readers who need to know the basics of plane trigonometry [*]. Readers with a strong mathematical background may skip this chapter. Others will find it useful, as well as a convenient source for review.

4.1 Introduction

Trigonometry is the branch of mathematics that is concerned with the relationships between the sides and the angles of triangles. We will now define angle and radian formally.

An angle is an angular unit of measure with vertex (the point at which the sides of an angle intersect) at the center of a circle, and with sides that subtend (cut off) part of the circumference. If the subtended arc is equal to one-fourth of the total circumference, the angular unit is a right angle. If the arc equals half the circumference, the unit is a straight angle (an angle of 180 ). If the arc equals 1/360 of the circumference, the angular unit is one degree. An angle between 0 and less than 90 is called an acute angle, while an angle between 90 and less than 180 is called an obtuse angle.

Each degree is subdivided into 60 equal parts called minutes, and each minute is subdivided into 60 equal parts called seconds. The symbol for degree is ; for minutes, ; and for seconds, . In trigonometry, it is customary to denote angles with the Greek letters ? (theta) or ?

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