Name: Franklin Ronaldo Gustavo Bac Cuzalo
Card: 202145499
A) Answer the following questions (read pages 42-47).
What is another name for Trigonometric Functions?
also called circular functions
What is a RIGHT TRIANGLE?
In this use, trigonometric functions are used, for instance, in navigation, engineering, and physics.
What is a hypotenuse?
The hypotenuse is the side opposite the right angle, in this case side h. The hypotenuse is always
the longest side of a right-angled triangle
Which one is the opposite side?
The opposite side is the side opposite to the angle we are interested in (angle A), in this case side
a.
Which one is the adjacent side?
The adjacent side is the side having both the angles of interest (angle A and right-angle
C), in this case side b
What does the = mean in an equation? Why was this symbol invented?
In modern notation, this is written by placing the expressions on either side of an equals
sign (=). The = symbol was invented by Robert Recorde (1510-1558), who considered
that nothing could be more equal than parallel straight lines with the same length.
How are letters of the alphabet used in equations? What do they represent?
By convention, unknowns are denoted by letters at the end of the alphabet, x, y, z, while knowns
are denoted by letters at the beginning, a, b, c, d, ...
What is a Diophantine equation?
A Diophantine equation is an equation where the unknowns are required to be integers.
What is a Parametric Equation?
A parametric equation includes variables which are all functions of one or more common variables
(called parameters).
What is a graph of a function?
The graph of a function f is the set of all points in the plane of the form (x, f(x)). We could
also define the graph of to be the graph of the equation y = f(x). So, the graph of a
function if a special case of the graph of an equation.
Where are the values of an independent variable placed in a graph?
Normally, the values of the independent variable (generally the x-values) are placed on the
horizontal axis, while the values of the dependent variable (generally the y-values) are placed on
the vertical axis.
What is an abscissa?
Is the perpendicular distance of P from the y-axis.
B) Investigate about 5 famous Mathematicians, and their contributions to Math (those
contributions are still used now).
1) Tales de Mileto
We start with Thales, the greatest of mathematicians and for his research, considered the first true
mathematician in history. Although he was born in Miletus in the middle of 624 B.C., he was
educated in Egypt. His knowledge led him to delve into geometry, astronomy and philosophy, thus
developing deductive reasoning applied to his theorems. He proposed the mathematical formula
to calculate the height of a triangle and its divisions in equal parts.
2) Pitágoras
Famous for the Pythagorean Theorem, which is not only applied in trigonometry, but has been
used to create the most revolutionary technologies of our era. His interest in mathematical studies
originated from Thales of Miletus, who was his teacher. To such an extent that he followed in his
footsteps fully, thus creating the Pythagorean School in which, together with his disciples, he was
able to develop and verify his theorem.
3) René Descartes
René Descartes recognized as one of the most important physicists, mathematicians and
philosophers of his time, dedicated his life to analyzing how mathematical equations worked. In
the same way, he wrote texts in which he described each of his theories and hypotheses, which
came to give a new concept to this science. He is the creator of the Cartesian Coordinate System,
infinitesimal calculus, method of exponents, among others.
4) Sophie Germain
Sophie Germain was born in 1776 and as a mathematician, she became known under the
pseudonym M. Le Blanc. She dedicated her years to the theory of numbers and elasticity, which
led her to win the Extraordinary Prize for Mathematical Sciences. Both studies were and are used
in Fermat's Theorem.
5) Leonard Euler
Leonard Euler was born in the year 1707, from a very young age he showed interest in
mathematics, he carried out multiple experiments to verify his theories that he left written in
countless texts. His experiments focused on geometry, mechanics, the application of mathematics
in technology, among others. Of all, the one that had the greatest impact was Number Theory that
led him to be classified as the most important mathematician in the world.
