One of the largest issues in ancient mathematics was accurac

One of the largest issues in ancient mathematics was accuracy—nobody had calculators that went out ten decimal places, and accuracy generally got worse as the numbers got larger. Why did trigonometry allow for some questions to be answered very accurately, even if the numbers involved were very large?

Solution

Problem of accuracy arises when calculations involve repeating or non terminating decimals. trigonometry allows us to use ratios like sin, cos, or tan to accurately represent values in ratio form that can be further used for new calculation which allows more accurate results. There is Pythagorean theorem too that help us represents one side of triangle in form of others using formula c^2=a^2+b^2 where c is hypotenuse in right angle. There are many uses of trigonometry in various fields to accurately represent larger repeating and not terminating decimals.