Triangle - Using trigonometry

Triangle - Using trigonometry: Encyclopedia - Triangle

A triangle is one of the basic shapes of geometry: a two-dimensional figure with three vertices and three sides which are straight line segments. Triangle - Types of triangles. Triangles can be classified according to the relative lengths of their sides: In an equilateral triangle all sides are of equal length. An equilateral triangle is also equiangular, i.e. all its internal angles are equal—namely, 60°; it is a regular polygon In an isosceles triangle two sid ...

Including:

Triangle - Non-planar triangles

Read more here: » Triangle: Encyclopedia - Triangle

Triangle - Using trigonometry: Encyclopedia II - Triangle - Computing the area of a triangle Calculating the area of a triangle is an elementary problem encountered often in many different situations. Various approaches exist, depending on what is known about the triangle. What follows is a selection of frequently used formulae for the area of a triangle. Triangle - Using geometry. The area S of a triangle is S = ½bh, where b is the length of any side of the triangle (the base) and h (the altitude) is the perpendicular distance between the base and the vertex not on the base. ...

Including:

Trigonometric function - Relationship to exponential function

Trigonometric function - Definitions via differential equations

Trigonometric function - The significance of radians

Triangle - Using trigonometry: Encyclopedia - Aristarchus On the Sizes and Distances

On the Sizes and Distances [of the Sun and Moon] is the only extant work written by Aristarchus of Samos, an ancient Greek astronomer who lived circa 310 BC - 230 BC. In this work, he calculates the sizes of the Sun and Moon, as well as their distances from the Earth in Earth radii. Aristarchus On the Sizes and Distances - Symbols. His method relied on several very difficult observations: The angle between the sun and moon when the moon is exactly half lit The apparent size of t ...

Including:

Triangle - Using trigonometry: Encyclopedia - Unit circle

In mathematics, a unit circle is a circle with unit radius, i.e., a circle whose radius is 1. Frequently, especially in trigonometry, "the" unit circle is the circle of radius 1 centered at the origin (0, 0) in the Cartesian coordinate system in the Euclidean plane. The unit circle is often denoted S1; the generalization to higher dimensions is the unit ball. If (x, y) is a point on the unit circle in the first quadrant, then x and y are the lengths of the legs of a right triangle whose hypotenuse has length 1. Thus, by the Pythagorean theorem, x and ...

Including:

Triangle - Using trigonometry: Encyclopedia - Angle

An Angle (from the Lat. angulus, a corner, a diminutive, of which the primitive form, angus, does not occur in Latin; cognate are the Lat. angere, to compress into a bend or to strangle, and the Greek ἀγκύλος (angulοs) crooked, curved; both connected with the Aryan or Indo-European root ank-, to bend) is the figure formed by two rays sharing a common endpoint, called the vertex of the angle. Angles provide a means of expressing the difference ...

Including:

Read more here: » Angle: Encyclopedia - Angle

Triangle - Using trigonometry: Encyclopedia - Aryabhata

Aryabhata (आर्यभट) Āryabhaṭa) is the first of the great astronomers of the classical age of India. He was born in 476 AD in Ashmaka but later lived in Kusumapura, which his commentator Bhāskara I (629 AD) identifies with Pataliputra (modern Patna). His book, the Āryabhatīya, presented astronomical and mathematical theories in which the Earth was taken to be spinning on its axis and the periods of the planets were given with respect to the sun (in other words, it was heliocentric).He believes that the Mo ...

Including:

Aryabhata - Overview

Triangle - Using trigonometry: Encyclopedia - Gersonides

Levi ben Gershon ("Levi son of Gerson"), better known as Gersonides or the Ralbag (1288-1344), was a famous rabbi, philosopher, mathematician and Talmudic commentator. He was born at Bagnols in Languedoc, France. Gersonides - Biography. As in the case of the other medieval Jewish philosophers little is known of his life. His family had been distinguished for piety and exegetical skill in Talmud, but though he was known in the Jewish community by commentaries on certain books of the Bible, he n ...

Including:

Gersonides - Bibliography

Triangle - Using trigonometry: Encyclopedia II - Trigonometric function - Properties and applications

The trigonometric functions, as the name suggests, are of crucial importance in trigonometry, mainly because of the following two results: Trigonometric function - Law of sines. The law of sines for an arbitrary triangle states: It can be proven by dividing the triangle into two right ones and using the above definition of sine. The common number (sinA)/a occurring in the theorem is the reciprocal of the diameter of the circle through the three points ASee also:

Triangle - Using trigonometry: Encyclopedia II - Trigonometric function - Properties and applications

The trigonometric functions, as the name suggests, are of crucial importance in trigonometry, mainly because of the following two results: Trigonometric function - Law of sines. The law of sines for an arbitrary triangle states: It can be proven by dividing the triangle into two right ones and using the above definition of sine. The common number (sinA)/a occurring in the theorem is the reciprocal of the diameter of the circle through the three points ASee also:

Triangle - Using trigonometry: Encyclopedia II - Spherical trigonometry - Identities

Spherical triangles satisfy a spherical law of cosines cosc = cosacosb + sinasinbcosC. The identity may be derived by considering the triangles formed by the tangent lines to the spherical triangle subtending angle C and using the plane law of cosines. Moreover, it reduces to the plane law in the small angle limit. They also satisfy ...

Dream Sharing Forum

Triangle - Using trigonometry

A Wisdom Archive on Triangle - Using trigonometry

ARTICLES RELATED TO Triangle - Using trigonometry

Including:

See also:

See also:

Including:

Including:

Including:

Including:

Including:

Including:

See also:

See also:

See also:

See also:

See also:

See also:

See also:

See also:

See also:

Rate this archive!