“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
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
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.”
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