The sin function has Indian and Greek roots. Part of that history is in the name 'sin' itself. I will let you all look that up. It's quite a funny story especially the jya to jayb bit.
This comment is about computation of sin in Indian mathematics and its definition.
The analogue of the sin function in Indian mathematics was a function from length to length. It was defined as the length of the half chord that corresponds to the angle, not of a unit radius circle but of a circle of radius 3438 units.
But why 3438 ?
That requires understanding the Indian system of measuring angles by length.
They wanted to have a numeric precision of 1 arc minute but weren't very fond of manipulating fractions. So they incorporated their requirement in how they standardized their circle -- Not by radius or diameter but by arc length. They chose that circle to be the standard for which the arc length of one arc minute is unit length.
If one does the math, it is 360 * 60 / 2π. Plugin the accuracy of π that was known to Indian mathematicians of that time you get a radius of 3438 units.
If you are curious about their numeric calculation of sin look up Aryabhatta and Bhaskara. Wikipedia is quite informative.
The sin function has Indian and Greek roots. Part of that history is in the name 'sin' itself. I will let you all look that up. It's quite a funny story especially the jya to jayb bit.
This comment is about computation of sin in Indian mathematics and its definition.
The analogue of the sin function in Indian mathematics was a function from length to length. It was defined as the length of the half chord that corresponds to the angle, not of a unit radius circle but of a circle of radius 3438 units.
But why 3438 ?
That requires understanding the Indian system of measuring angles by length.
They wanted to have a numeric precision of 1 arc minute but weren't very fond of manipulating fractions. So they incorporated their requirement in how they standardized their circle -- Not by radius or diameter but by arc length. They chose that circle to be the standard for which the arc length of one arc minute is unit length.
If one does the math, it is 360 * 60 / 2π. Plugin the accuracy of π that was known to Indian mathematicians of that time you get a radius of 3438 units.
If you are curious about their numeric calculation of sin look up Aryabhatta and Bhaskara. Wikipedia is quite informative.
https://en.wikipedia.org/wiki/%C4%80ryabha%E1%B9%ADa's_sine_...
https://en.wikipedia.org/wiki/Bh%C4%81skara_I%27s_sine_appro...