ENGTRIG: LECTURE # 4.2 Spherical Trigonometry Spherical Trigonometry Engr. Christian Pangilinan Areas of a Spherical Triangle A= π R2 E 180o E R E = A + B + C − 180o Where: spherical excess radius of the sphere Spherical Triangles Part of the surface of the sphere bounded by three arcs of three great circles Right Spherical Triangle – a spherical triangle containing at least one right angle If the sides are known instead of the angles‚ then L’Huiller’s Formula can be used
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Algebra is a way of working with numbers and signs to answer a mathematical problem (a question using numbers) As a single word‚ "algebra" can mean[1]: * Use of letters and symbols to represent values and their relations‚ especially for solving equations. This is also called "Elementary algebra". Historically‚ this was the meaning in pure mathematics too‚ like seen in "fundamental theorem of algebra"‚ but not now. * In modern pure mathematics‚ * a major branch of mathematics which
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consequently known as "the father of trigonometry."[3] Sumerian astronomers introduced angle measure‚ using a division of circles into 360 degrees.[4]They and their successors the Babylonians studied the ratios of the sides of similar triangles and discovered some properties of these ratios‚ but did not turn that into a systematic method for finding sides and angles of triangles. The ancient Nubians used a similar methodology.[5] The ancient Greeks transformed trigonometry into an ordered science.[6] Classical
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The Way Trigonometry is used in Astronomy By: Joanna Matthews Practical Applications of Advanced Mathematics Mrs. Amy Goodrum July 15‚ 2003 Abstract This report is about how trigonometry is used in Astronomy. Even though trigonometry is applied in many areas‚ such as engineering‚ chemistry‚ surveying‚ and physics‚ it is mainly used in astronomy Trigonometry is used to find the distance of stars‚ the distance from one planet to another and from one plant to the sun. It is possible to find the
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non-scientists‚ trigonometry is known chiefly for its application to measurement problems‚ yet is also often used in ways that are far more subtle‚ such as its place in the theory of music; still other uses are more technical‚ such as in number theory. The mathematical topics of Fourier series and Fourier transforms rely heavily on knowledge of trigonometric functions and find application in a number of areas‚ including statistics. There is an enormous number of applications of trigonometry and trigonometric
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ter------------------------------------------------- A Brief History of Trigonometry A painting of the famous greek geometrist‚ and "father of measurement"‚ Euclid. In the times of the greeks‚ trigonometry and geometry were important mathematical principles used in building‚ agriculture and education. The Babylonians could measure angles‚ and are believed to have invented the division of the cirle into 360º.[1] However‚ it was the Greeks who are seen as the original pioneers of trigonometry. A Greek mathematician‚ Euclid‚ who
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Spherical trigonometry Spherical trigonometry is that branch of spherical geometry which deals with the relationships between trigonometric functions of the sides and angles of the spherical polygons (especially spherical triangles) defined by a number of intersecting great circles on the sphere. Spherical trigonometry is of great importance for calculations in astronomy‚ geodesy and navigation. The origins of spherical trigonometry in Greek mathematics and the major developments in Islamic mathematics
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Aminata Kamara Week II Assignment 22 November 2012 This week assignment required to solve problem 68 on page 539 of Elementary and Intermediate Algebra. There are three part to this assignment and the first part is as follows; The accompanying graph shows all of the possibilities for the number of refrigerators and the number of TVs that will fit into an 18-wheeler. | | a) | Write an inequality to describe this region. | p = y1-y2 / X1-x2 = 330 – 0 / 0-110 = -3/1 the slope
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SPHERICAL TRIGONOMETRY DEFINITION OF TERMS The sphere is the set of all points in a three-dimensional space such that the distance of each from a fixed point is constant. The fixed point and the given distance are called the center and the radius of the sphere respectively. The intersection of a plane with a sphere is a circle. If the plane passes through the center of the sphere‚ the intersection is a great circle; otherwise‚ the intersection is a small circle. A line perpendicular to
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what is required for a diploma. The four math classes in discussion are Algebra 1‚ Geometry‚ Algebra 2‚ and Trigonometry. Trigonometry is usually the last class that could be required. Although Trigonometry contains useful information‚ it shouldn’t be required for a diploma because of economic‚ scientific‚ and personal reasons. The main reason for teaching math is to apply in the real world. It seems at the least Algebra 1‚ Algebra 2‚ and Geometry is absolutely necessary for solving the area and sides
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