Pythagoras often receives credit for the discovery of a method for calculating the measurements of triangles, which is known as the Pythagorean theorem. However, there is some debate as to his actual contribution the theorem.Know More
Pythagoras was an Ionian Greek philosopher, mathematician and religious scholar. His greatest contribution to mathematics is the Pythagorean theorem. The theorem states that in a right triangle, the area of the square of the hypotenuse, which is the side across from the right angle, is equal to the sum of the square of the areas of the other two sides. Despite the theorem bearing his name, Pythagoras was not the first person to use this calculation. This computation was in use in Mesopotamia and India long before Pythagoras lived. There is some speculation that Pythagoras and his students are responsible for the first proof of the theorem. However, given that it was the nature of Pythagoras' students to attribute everything to their teacher, it is unclear if Pythagoras himself ever worked on the proof.
Besides mathematics, Pythagoras made contributions to religion and music. Pythagoras and his followers believed that souls did not die but went through a cycle of rebirth that ended when purity of life was obtained. Pythagoras' beliefs placed great emphasis on a lifelong search for salvation. Pythagoras might also be responsible for an understanding of string length in relation to tone in musical instruments.Learn more about Trigonometry
Evaluating sin(arc-tan x) is a simple process that involves two steps: using a right-angled triangle to label the two sides and the angle in question, which is x, and using the Pythagoras theorem to calculate the remaining side and calculating the function from these values. Writing out the expression in words is the starting point of evaluating it. In this case, it is the sine of Arc-tan x.Full Answer >
The tangent-secant theorem states that if two secant segments share an endpoint outside of a circle, the product of one segment length and the length of its external segment equals the product of the other segment's length and the length of its external segment. It is a special subtype of another mathematical theorem: the power of a point theorem.Full Answer >
Successfully working through trigonometry problems requires knowledge of the properties of triangles as well as the ability to measure and understand the ratios called sine, cosine and tangent. Using equations associated with the ratios, it is possible to find the angles and lengths of right angle triangles.Full Answer >
Simplifying trigonometric expressions is a matter of understanding the circles and triangles upon which trigonometry is based. While much of the simplification can be done geometrically, knowledge of trigonometric identities will allow an algebraic solution.Full Answer >