Do we really need a calculator to find the sine of 1 degree?

In today’s education system, students rely so much on computers and calculators that they even let these technological tools handle the most basic algebraic operations like addition and subtraction. Some even think that the very first item needed to solve a math or science problem is a calculator. This unfortunate thought and extreme dependence on technology eventually leads to the hindrance of cognitive abilities, the deterioration of critical thinking and the loss of scientific intuition. Understanding and employing the technology is different than putting it ahead of our knowledge and thinking. In this study, we do not intend to depreciate the role of technology in our lives, but to value the basic knowledge in mathematics. We would like to show all readers how valuable the accumulated knowledge and the methods developed over the centuries by great mathematicians and scientists are. We also want to note that the technology could only be present due to this collective knowledge of humankind. In this regard, we demonstrate how to estimate values of various irrational numbers, such as those arising from square root operations and those as the outcomes of trigonometric functions, without using a calculator.

Without any doubt, technology takes up a great part of our lives. There is not a single day passed that we come across something new which makes our lives more comfortable than the day before. Therefore, it is quite important to become technology literate so as to have the ability to use, manage and understand the existing technological tools, and even to invent the future ones. Our main objective is to guide the youth towards becoming technology literate in their lives. In this regard, we intend to show why basic knowledge in mathematics is paramount, where this knowledge not only helps us understand how the technology is developed via the employment of fundamental principles, but also provides us with an immense power to accomplish certain tasks without any need of sophisticated tools.

Technology is obviously useful and needed. It is also a manifestation of collective human knowledge, and it is there to ease our tasks. However, in order to become technology literate, one should understand the underlying principles that make the technological tools run. In this study, we will show how amazing things we can do using the principles and knowledge based upon which calculators are developed by estimating the numerical values for the square roots of real numbers and the values of the trigonometric functions of real angles. In doing so, we will derive several trigonometric identities, introduce Intermediate Value Theorem and Newton’s Iterative Method. As the title suggests, in the final step we will give a highly accurate and precise estimate for the value of sine 1 degree. All will be done by just using basic four operations (addition, subtraction, multiplication and division) and some knowledge of calculus.


(Below are some sample pages)

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