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The word "trigonometry" comes from two Greek words meaning "triangle measure." Trigonometry concerns the relationships among the sides and angles of triangles. It also concerns the properties and applications of these relationships, which extend far beyond triangles to real-world problems.

Evidence of a knowledge of elementary trigonometry dates to the ancient Egyptians and Babylonians. Led by Ptolemy, the Greeks added to this field of knowledge during the first millennium B.C.E.; simultaneously, similar work was produced in India. Around 1000 C.E., Muslim astronomers made great advances in trigonometry. Inspired by advances in astronomy, Europeans contributed to the development of this important mathematical area from the twelfth century until the days of Leonhard Euler in the eighteenth century.

## Trigonometric Ratios

To understand the six trigonometric functions, consider right triangle *ABC* with right angle *C.* Although triangles with identical angle measures may have sides of different lengths, they are...

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