Question 971852: Hello Tutor, I really need your help to answer this question please.
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?
Found 2 solutions by josmiceli, casdyx:
Answer by josmiceli(19441)   (Show Source):
Answer by casdyx(1)  (Show Source):
You can put this solution on YOUR website! Trigonometry allowed for some questions to be answered accurately even if the numbers were very large simply because the accuracy of the numbers can only be derived when the magnitude and degree of the numbers are fully accounted for in the solution. The ancient mathematician could provide trigonometric theorems with formula and equations they presented which they used to determine the exact measurement and calculation of any given trigonometric problems.
The study of trigonometric ratio accommodated degrees, radiants and values of whole identities which are easily used to quantify large numbers. One example of this is Pi. With the used of pi numbers can exactly be presented. The expansion of 2pi may give non terminating decimals but the simple expression of 2pi can solve the problem.
Also the use of pythagoras' theorem largely assisted the ancient mathematician to determine the accuracy of numbers and measurement of the lengths of a right-angled triangles. The theorem helped to note that the square of the side of hypotheneus is equal to the sum of the squares of the two other sides. For instance, they could use the accuracy of the pythagoras' theorem to get the accurate length of the line of hypotheneus of a right angle-triangle with Sides 6cm and 8cm.
This theorem assisted to get the accuracy length by squaring the two given sides and getting the squares which is equivalent to the square of the hypotheneus. That is y^2 = 6^2 + 8^2. With this, the accurate answer of the hypotenuse is derived even if the number involved is very large. Throght this discovery, they knew things like 10cm, 6cm, 8cm right-angle triangle existed because 10^2 = 6^2 + 8^2.
They also new all the trig-ratios and trig-functions of angles of in the trigonometry. Consider, the case of sin(B) = 8/10 for the angle opposite the side 8cm with the hypotenuse 10cm long.
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