Beating About the Bush in Math Class is a Dangerous Proposition

This was an essay I was told to write by my English teacher... she supplied the topic. This was the first thing that came out of my mind :)

Mathematics is a subject dealing with numbers. Numbers are such things that many functions can be done to. There are thousands of possible functions that can be done to a number or numbers, such as addition, subtraction, multiplication, division, exponents, sine, cosine, tangent, etc.  Many of these functions are actually combinations of other functions, for example, multiplication is just adding a number to itself over and over again. Also, a result of a function can sometimes be found by doing a different function or set of functions to the same number. However, it has been found that it is the easiest and most accurate to use as few functions as possible while trying to get an answer of a mathematics problem.

For example, say we want to find the area of a right-angled triangle of height 10 centimeters, base 5 centimeters, and one angle of size 63.44 degrees. The simplest formula to find the area is to multiply the height and base, then to divide the answer by 2. If we use this combination of functions, then we find that the area of the triangle in question is 25 square centimeters.

We can also find the area by calculating the height using trigonometry. Say that the 63.44 degree angle is in such a place that it is made by the base and the hypotenuse. Therefore, the tangent of the 63.44 degree angle is height/base. The tangent of a 63.44 degree angle is 2. Therefore, 2=height/5 (5 is the base). Therefore, the height is 10. Then, using the formula, we find that the area of this triangle is 25 centimeters.

We got the same answer for both the methods. However, the first way was much easier. Since there were fewer functions involved, there was less scope of error. In the second method, we beat about the bush, and wasted time. If we made a mistake in the trigonometry, then our height would be wrong also, and thus our final answer would be incorrect. Also, trigonometry requires a calculator, so we couldn’t have used the second method if we didn’t have a calculator on hand. It also took more time, so if this question came in a test, then we would lose out on time to do the rest of the paper.

When using more functions, in many places, long decimal values can become unmanageable, and so we would have to round off values. When rounding of values, they become more inaccurate, and the final answer becomes very inaccurate. Using fewer functions means not having to round off values in your working very often, so your answer will be more accurate,

Thus, it can be seen that beating about the bush in math class is a dangerous proposition!

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