Trigonometry

Trigonometry was probably developed for use in sailing as a navigation method used with astronomy.[2] The origins of trigonometry can be traced to the civilizations of ancient Egypt, Mesopotamia and the Indus Valley (India), more than 4000 years ago.[citation needed] The common practice of measuring angles in degrees, minutes and seconds comes from the Babylonian's base sixty system of numeration. The first recorded use of trigonometry came from the Hellenistic mathematician Hipparchus[1] circa 150 BC, who compiled a trigonometric table using the sine for solving triangles. Ptolemy further developed trigonometric calculations circa 100 AD. The ancient Sinhalese in Sri Lanka, when constructing reservoirs in the Anuradhapura kingdom, used trigonometry to calculate the gradient of the water flow. Archeological research also provides evidence of trigonometry used in other unique hydrological structures dating back to 4 BC.[citation needed] The Indian mathematician Aryabhata in 499, gave tables of half chords which are now known as sine tables, along with cosine tables. He used zya for sine, kotizya for cosine, and otkram zya for inverse sine, and also introduced the versine. Another Indian mathematician, Brahmagupta in 628, used an interpolation formula to compute values of sines, up to the second order of the Newton-Stirling interpolation formula. In the 10th century, the Persian mathematician and astronomer Abul Wáfa introduced the tangent function and improved methods of calculating trigonometry tables. He established the angle addition identities, e.g. sin (a + b), and discovered the sine formula for spherical geometry: : Also in the late 10th and early 11th centuries, the Egyptian astronomer Ibn Yunus performed many careful trigonometric calculations and demonstrated the formula : Persian mathematician Omar Khayyám (1048-1131) combined trigonometry and approximation theory to provide methods of solving algebraic equations by geometrical means. Khayyam solved the cubic equation x3 + 200x = 20x2 + 2000 and found a positive root of this cubic by considering the intersection of a rectangular hyperbola and a circle. An approximate numerical solution was then found by interpolation in trigonometric tables. Detailed methods for constructing a table of sines for any angle were given by the Indian mathematician Bhaskara in 1150, along with some sine and cosine formulae. Bhaskara also developed spherical trigonometry. The 13th century Persian mathematician Nasir al-Din Tusi, along with Bhaskara, was probably the first to treat trigonometry as a distinct mathematical discipline. Nasir al-Din Tusi in his Treatise on the Quadrilateral was the first to list the six distinct cases of a right angled triangle in spherical trigonometry. In the 14th century, Persian mathematician al-Kashi and Timurid mathematician Ulugh Beg (grandson of Timur) produced tables of trigonometric functions as part of their studies of astronomy. The mathematician Bartholemaeus Pitiscus published an influential work on trigonometry in 1595 which may have coined the word "trigonometry" itself. Hope that helps. :)

A triangular based pyramid has four vertices and four faces

They use it to measure angles and lengths

a pyramid does.

three
3.

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An octagon, a cube, a seven-sided pyramid.

360 degrees

The point where the x-axis and the y-axis meet is called the origin.

It allowed points in space to be described algebraically. This allowed lines and curves to be described using algebra. Bringing together algebra and geometry meant that tools that mathematicians had developed for solving algebraic problems could be applied to problems in geometry and tools from geometry could be applied to algebra.

16

It is the origin

triangular prism

Before calculators, trig functions in general were evaluated using a slide rule (fast, but accurate to only 2-3 significant digits, and interpolation tables, which required interpolating between values in a printed table of function values to get up to 3-4 significant digits. Tricks were a big part of the repertoire - for example for small angles of less than about 7 degrees, sin and tangent are equal to the angle in radians.

Spherical geometry was fairly labor intensive, to say the least, since several trig functions are used for even simple distance and angle calculations. Special tables were printed for common cases, such as plotting great circle distances and bearings for terrestrial navigation.

In a desert island setting, given infinite time and desire, trig functions can be calculated using various converging series, with the Taylor series being a commonly taught (though slow!) example.

It is a semi-circular arc joining two diametrically opposite points on the sphere. These may be the "North" and "South" poles.

It is the sum of its 4 sides

Trigonometry is the study of angles ond lengths. If you know one angle and one side length of a right traingle, you can find all the other values. If you know your distance from a tall object, and the angle made by the base of the tall object, your feet, and the top of the object, you can find the height of the object.

Calculus

Trigonometry is used in the fields of design, music, navigation, cartography, manufacturing, physics, optics, projectile motion, and any other field which involves angles, fields, waves, harmonics, and vectors.

Simply put, a vector is 2 dimensional.

Think of speed - it is only one dimensional. It is not a vector, it is a scalar. It is measured in a scale, most commonly noticed when inside a vehicle. You are travelling at 100km/h (60mph)

Vectors are 2 dimensional, they have a magnitude and a direction.

Think of velocity, as an arrow - imagine you are travelling at 60 mph in a northerly direction, your arrow would be pointing to the notth, with a magnitude of 60mph, If you were travelling at 60mph in a southerly direction, your velocity vector would be pointing towards the south, the exact opposite of your vector if you were travelling in a northerly direction.

However the speed in these two scenario's, speed not being a vector, remains exactly the same, 60mph.

Trigonometry was first used by the ancient Babylonians and Egyptians. Babylonians used it primarily in their astronomical calculations and there is some debate over whether this was actually trigonometry or some other form of calculation. However, the Egyptians did use a primitive form of trigonometry while building the pyramids. A scribe known as Ahmes actually performed a trigonometric solution in his "The Rhind Mathematical Papyrus"

1

Trigonometry is used very extensively in engineering. It is used to break force vectors into components, allowing civil and construction engineers to see how stress is channeled throughout a building. It is used to model sound and light waves, which is a useful tool for acoustic and optic engineers. It is also used extensivly in electrical engineering to find the strengths of fields.