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assuredlonewo
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How where all the possible tangents, cosines, and sines of angles found?
micromass said:Hi assuredlonewo
What do you mean with this question. I understand it in three ways:
- How did they come up with the concept of sine
- how did they find the sine of a specific nice angle, say 45°
- how do they find the sine of all possible angles
Which of these (if any) do you mean?
Deveno said:it was not uncommon, even into the 20th century, for most people using sines to reference tabulated values.
The original formulas for tangent, cosine, and sine were derived using geometric constructions and ratios in ancient civilizations like Babylon, Egypt, and India. These civilizations used these trigonometric functions for practical purposes such as astronomy and surveying.
The relationship between tangents, cosines, and sines was first discovered by the Greek mathematician Hipparchus in the 2nd century BC. He developed the first known trigonometric table, which contained values for the tangent function.
Trigonometry evolved over time as more mathematicians, such as Ptolemy and Aryabhata, contributed to its development. They expanded upon Hipparchus' work and introduced new trigonometric identities and functions. In the 16th century, the concept of radians was introduced, which greatly simplified the calculation of trigonometric functions.
Modern methods for calculating tangents, cosines, and sines use advanced mathematical techniques such as calculus, complex numbers, and computer algorithms. These methods allow for more accurate and efficient calculations compared to the geometric constructions used in ancient times.
Trigonometry has countless practical applications in fields such as engineering, physics, astronomy, and navigation. It is used to calculate distances and angles, design structures, and analyze wave patterns. It is also essential in the development of technologies such as GPS and radar.