Guest Post: Calculating Trignometric Values

Many students who start to learn Trigonometry often ask themselves how do we come to know that

\sin 30^\circ = \frac{1}{2} or \cos 45 ^\circ = \frac{\sqrt{2}}{2}

or for that matter any other trigonometric value?

Most of us would say use a trigonometric table or use a scientific calculator and you get the value. That’s okay, but the question still remains unanswered. How does a calculator come to know that \tan 15^\circ = 0.26794919... or how did the mathematicians create the entire trig tables when calculators were not invented? There should be some formula that tells us as to how the values are calculated. More importantly, can I, using a standard calculator, find the approximate value of let’s say \sin 50.5^\circ? Yes, there is a simple formula to find the value of sine of any acute angle. Though the formula does not give accurate results, it comes handy to know the value of \sin \theta  where 0^\circ \leq \theta \leq 90^\circ.

 \sin x ^\circ = \frac{4x(180 - x)}{40500 - x(180 - x)}.

This rational approximate formula was discovered by Bhaskara I of India in the seventh century. This simple formula enables us to calculate the sine of any given acute angle (any even obtuse angle) with a maximum absolute error of 0.00163.  » Read more

Book of Proof: A Very Good Introductory Book to Mathematical Proofs

Two weeks ago, I finished reading Book of Proof  (link goes to Amazon) by Professor Richard Hammack, and so far, it was the best book that I have read about introduction to mathematical proofs. I recommend this book to high school students who are interested in pursuing a mathematics degree, to college students who are math majors, and to teachers who will teach or who are teaching an introductory course on mathematical proofs. Here are some of the reasons why I really like this book.

Clear Explanations

The explanations of concepts in this book are very clear and the concepts are well-connected. Maybe this is because the author’s long experience in teaching this course (or maybe he is just a very good teacher). This book is a product of the author’s lecture notes on teaching mathematical proofs for the past 14 years.  » Read more

Free Peer-Reviewed Math Ebooks from OpenStax

If you are looking for free math resources, I found a website that offers peer-reviewed math ebooks for college and AP Courses. This website is OpenStax which is based in Rice University and supported by several foundations. Below are the links to the math ebooks.

Aside from the math ebooks on Science, Social Science, Humanities, and AP Courses are available on the website.

For more free resources, you can visit Math and Multimedia’s All for Free page.

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