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I can remember roughly how to differentiate a standard xy formula but sines , cosines and tangents are a mystery.
This same table was reproduced in the work of Brahmagupta and detailed method for constructing a table of sines for any angle were give by Bhaskara in 1150.
If you use the distance along the ground, you have to find the vertical component by multiplying by the sine of the angle of the hill in both the distance and acceleration terms.
It presents a one-point iterative technique for calculating the sine of a given angle.
A mathematical function, like sine or logarithm, gives the same answer to a particular question each time you ask it.
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