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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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 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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RIGHT TRIANGLE TRIGONOMETRY The word Trigonometry can be broken into the parts Tri‚ gon‚ and metry‚ which means “Three angle measurement‚” or equivalently “Triangle measurement.” Throughout this unit‚ we will learn new ways of finding missing sides and angles of triangles which we would be unable to find using the Pythagorean Theorem alone. The basic trigonometric theorems and definitions will be found in this portion of the text‚ along with a few examples‚ but the reader will frequently
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Trigonometry‚ 8th ed; Lial‚ Hornsby‚ Schneider Trigonometry Final Exam Review: Chapters 7‚ 8‚ 9 Note: Trig Final Exam Review F07 O’Brien A portion of Exam 3 will cover Chapters 1 – 6‚ so be sure you rework problems from the first and second exams and from the Exam 1 and Exam 2 Reviews. Work these problems with no resources other than the departmental formula sheet and a graphing calculator. Your book‚ notebook‚ homework‚ solutions manual‚ etc. should be closed. Read and carefully follow all
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Trigonometry Trigonometry uses the fact that ratios of pairs of sides of triangles are functions of the angles. The basis for mensuration of triangles is the right- angled triangle. The term trigonometry means literally the measurement of triangles. Trigonometry is a branch of mathematics that developed from simple measurements. A theorem is the most important result in all of elementary mathematics. It was the motivation for a wealth of advanced mathematics‚ such as Fermat’s Last Theorem
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Pitogo High School Pre-calculus 2nd QT Mastery Test #1 Name: _____________________________________________ Date: _________________ Yr.&Sec.: _____________________________________________ Teacher: _________________ Direction: Read the following then answer correctly. Write your answer & solutions on a separate answer sheet. A. True or False. ______1. The area of a triangle equals one-half the product of two of its side lengths and the sine of the angle. ______2. Given only the three
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on what math classes are required for a high school diploma. Each state has its own rules for 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
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supporting cable of length 30 m is fastened to the top of a 20m high mast. What angle does the cable make with the ground? How far away from the foot of the mast is it anchored to the ground? Solution We can use Pythagoras’ Theorem but we shall use trigonometry here. We first find the
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ANSWER: 8-4 Trigonometry Express each ratio as a fraction and as a decimal to the nearest hundredth. 1. sin A 3. cos A SOLUTION: The cosine of an angle is defined as the ratio of the adjacent side to the hypotenuse. So‚ ANSWER: SOLUTION: The sine of an angle is defined as the ratio of the opposite side to the hypotenuse. So‚ 4. tan A ANSWER: 2. tan C SOLUTION: The tangent of an angle is defined as the ratio of the opposite side to the adjacent side. So‚ ANSWER: 3. cos A SOLUTION:
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