College Algebra & Trigonometry, 2018a

Chapter 8
Right Triangle Trigonometry
The Origins of Trigonometry
The precursors to what we study today as Trigonometry had their origin in ancient
Mesopotamia, Greece and India. These cultures used the concepts of angles
and lengths as an aid to understanding the movements of the heavenly bodies
in the night sky. Ancient trigonometry typically used angles and triangles that
were embedded in circles so that many of the calculations used were based on
the lengths of chords within a circle. The relationships between the lengths of the
chords and other lines drawn within a circle and the measure of the corresponding
central angle represent the foundation of trigonometry - the relationship between
angles and distances.
The earliest values for the sine function were calculated by Indian mathematicians
in the 5th century. The cosine and tangent, as well as the cotangent, secant
and cosecant were developed by Islamic mathematicians by the 11th century. European
navigators used these ideas extensively to help calculate distances and
direction during the Middle Ages. Modern European trigonometry as we understand
it was then developed throughout the Renaissance (1450-1650) and Enlightenment
(1650-1800).
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