The Greeks developed a precursor to trigonometry by studying chords in a circle. However, the systematic tabulation of trigonometric ratios was conducted later by the Indian and Arabic mathematicians. It was not until about the 15th century that a 'modern' approach to trigonometry appeared in Europe. Two of the original motivations for the study of the sides and angles of a triangle were astronomy and navigation. These were of fundamental importance at the time and are still very relevant today. With the advent of coordinate geometry, it became apparent that the standard trigonometric ratios could be graphed for angles from 0 to 90 degrees. Using the coordinates of points on a circle, the trigonometric ratios were extended beyond the angles found in a right-angled triangle. It was then discovered that the trigonometric functions are periodic and so can be used to model periodic behavior in nature and in science generally. In this module, we will revise the basics of triangle trigonometry, including the sine and cosine rules, and angles of any magnitude. We then introduce radian measure, which is a natural way of measuring angles using arc length. This is absolutely essential as a prerequisite for the calculus of the trigonometric functions and also gives us simple formulas for the area of a sector, the area of a segment and arc length of a circle.
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