Three Basic Trig Functions Of Trigonometry

Being one of the greatest philosophers of his time, Pythagoras created a society of skilled mathematicians who worked together to facilitate mathematics, showed how numbers can be independent, and proved the Pythagorean theorem, making him iconic in mathematics today. His discoveries of simple yet essential methods are prevalent today throughout many mathematical fields in which they are treasured.

Pythagoras made influential contributions to philosophy and religion in the late 6th century BC. He is often revered as a great mathematician and scientist and is best known for the Pythagorean theorem which relates the two sides of a triangle to the hypotenuse using the formula a squared plus b squared equals c squared. However, because legend and obfuscation cloud his work even more than that of other pre-Socratic philosophers, one can give only a tentative account of his teachings, and some have questioned whether he contributed much to mathematics or natural philosophy. Many of the accomplishments credited to Pythagoras may actually have been accomplishments of his colleagues and successors. Some accounts mention that the philosophy associated with Pythagoras was related to mathematics and that numbers were

He used logic and reasoning to investigate the nature of the universe. Ptolemy’s model helped get people thinking about the universe being eternal, finite, and spherical. This document is most definitely not reliable because the conclusion was made without having all the needed information, and it was later disproved. A more accurate view could come from someone who does in depth studies of how the universe is actually laid out. As seen in Document 11, A Greek doctor by the name of Hippocrates became one of the first people that taught his belief that illnesses only had

Greek mathematical and scientific ideas have also been a large contribution. Euclid, a Greek mathematician, wrote many theorems. His theorems have been very substantial because they are included in today’s mathematical problems. One of his theorems include “If two straight lines cut one another, the vertical, or opposite, angles shall be equal.” This specific theorem is used in proofs and it proves that all vertical angles are equal. Hippocrates was a Greek physician who created the Hippocratic Oath. This oath

Hipparchus was a greek astronomer, geographer, and mathematician born 190 B.C. in Nicaea and died in 120 B.C. Rhodes, Rhodes, Greece. Hipparchus is accredited as the inventor of trigonometry because of his discovery of the first table of chords and also because he's the only person with valid data of the discovery and usage of trigonometry. In order to calculate the rising and setting of zodiacal signs, Hipparchus brought to light the division of circles into 360 degrees and the calculation of chords by looking at the triangles (spherical triangles or triangles that made up a circle) differently. Hipparchus experimented putting all triangles to be within a circle and with the three points each touching the

One of Thales’ most renounced findings include his discovery in geometric studies in the area reading the rules of triangles. He came to the conclusion that if the base angles of an isosceles triangle are equal, the sum of the angles of a triangle are equivalent to two right angles. With the application of “geometric principles to life situations, Thales was able to calculate the height of a pyramid by measuring its shadow, and the distance of a boat to the shore, by using the concept of similar triangles” (pg. 5, Muehlbauer). Realizations such as these helped shape the beginning for the formation of natural law based on observations of the world through explanation.

Failure is only an opportunity to begin again. To some, taking the Algebra 2 Trigonometry Regents Exam three times may seem like an abasement, but to me, each failure presented a chance to begin anew in achieving my goal; my Advanced Regents Diploma.

While researching “pre-industrial astronomical accomplishments,” it seemed that a good majority of the accomplishments being highlighted were those of the Mayan and Aztec civilizations. Feeling that these topics may be over-researched, I decided to turn my attention towards the accomplishments of those in a different area of the world. After switching my focus to the pre-industrial astronomical feats of ancient Greek scientists, I have found that in many cases, these scientists contributed more than one idea, finding, or apparatus to the field of astronomy. For this research, I decided to hone in on the contributions made by Greek scientist Hipparchus. Throughout his magnificent life, and all before the implementation of modern technology,

The Greeks made several inventions, most notably in the subject of math, which are still studied today and taught in school. Mathematician Euclid is often credited as the “Father of Geometry” for all his work and studies in this subject, which are compiled in his books called The Elements. He organized known geometrical statements called theorems and logically proved all of them. He proved the theorem of Pythagoras (another Greek mathematician), which stated that the equation (c2 = a2 + b2) is true for every right triangle.

There are six trigonometric ratios that one must know in order to find any angle in a right triangle. There are various of ways to remember these trigonometric ratios, but the most common way is through SOHCAOTOA. By having this clear in your memory, it will allow one to remember at least the three basic trigonometric ratios: Sine (sin.), Cosine (cos.), and Tangent (tan.). Before one learns about how SOHCAOTOA is split up, we must learn about the angles in a right triangle. First off, the hypotenuse is the longest line in a triangle, then in order to find the adjacent and opposite, one must locate where the angle. Upon locating the angle, we can conclude that the opposite is further away from the angle, whereas the adjacent is the closer one

Geometry first originated as a way to solve problems in architecture and navigation. A famous figure in geometry is Euclid. Around 300 BC, he published a book, The Elements, which contained definitions, axioms, and postulates that would be regarded as a standard of mathematical reasoning for the next two thousand years (Mueller, 1969). Euclid basically gave the foundation of what is now called Euclidean geometry. However,

During this time period many things were invented like the astrolabe, sextant, and caravel. The caravel was invented by the portuguese, was much less heavy so it could travel up rivers, was quicker for the longer journeys, and had a triangular sail instead of a rectangular sail. The astrolabe was an instrument that, in its earlier time, was used for astronomy and astrology but ended up mainly being used as a tool of navigation and to solve problems involving trigonometry, problems relating to time, and the position of the sun and stars. The astrolabe was invented by Hipparchus who lived from 190 BC - 120 BC and also made major contributions to trigonometry. Trigonometry is a type of math that involves the relations between a triangle’s angles and sides.

The Greeks and the Egyptians used triangles as early as 3500 BCE. They used these triangles as rules of thumb. They could apply these rules to specific applications. For example, the Egyptians knew that the 3:4:5 ratio was a right triangle. They could derive this because for them to create a right triangle the Egyptian land surveyors used a rope divided into twelve equal parts, creating a triangle with three pieces on one side, four pieces on the second side, and five pieces on the last side. The right angle was found where the three-unit side came together with the four-unit side. This was a very efficient way to create right triangles. It’s a mystery as to how the Egyptians came up with this, but this was later used by Pythagoras (c.571 -

Pythagoras developed the formula a2+b2=c2which is called the Pythagorean Theorem. They formula helps find the measure of the sides of a right triangle and is still used on a day to day basis in order for society to function. Overall, mathematics developed by the Greeks have been very useful to modern

Trigonometry is a branch of mathematics that studies the relationship between the sides and the angles of a triangle. The word trigonometry was derived from the Greek word trigonon which means triangle and metron for the word measure. While the other branch of mathematics, geometry which means earth and measurement, is concerned with the properties of space and figures.