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“Sine of an acute angle in a right triangle is the ratio of the opposite side to the hypotenuse. Let’s examine the properties of sine.”

Stop! Stop!! What a strange definition?! Where did it come from? Why do we need to study some sine? Is it only to pass an exam?

Dear reader! Do similar questions arise in your mind when you first face such definitions? Does an inner feeling of protest and some premature disgust appear towards these “sines”, with which you are deliberately tortured? If so, then this is the book for you. Our goal is to completely destroy such thoughts.

To achieve this goal, avoid formal style and dry language, and present material in a scientifically strong, yet lively and intuitive manner, we developed this book in the form of conversations between a father – an expert in the field, and his daughter and son.

The children are not familiar with trigonometry at all and do not have any special mathematical abilities. However, they do have one very valuable trait: they are curious.

We are deeply convinced that this is the most important quality you need to have to become a master of any subject.

The conversations between the father and his kids are written in a simple and casual language. You can consider these conversations as some sort of scientific “home” seminar, where the children argue, make mistakes, and sometimes unknowingly, make serious scientific discoveries. Therefore, by reading this textbook you will not only acquire knowledge about trigonometry, but will also see how science is “made”. During the course of learning, ask yourself this question: Would I have been able to come up with a certain result myself, or is it something completely incredible?

To emphasize the main initial idea of trigonometry about similarity of triangles, we decided to put on the cover page Curry’s puzzle modified by Martin Gardner1 and presented with his kind permission.

We hope that once you’ve read this book, you will say: “You know, trigonometry isn’t so disgusting after all. Actually, it is even beautiful.”

Alexander Rozenblyum

Leonid Rozenblyum

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