Subject: Topic: Contributions from various cultures and individuals: Trigonometry Example Right-triangle trigonometry Al-Tusi; Arabic mathematician (1200s): extended the pioneering work of the Greeks (Aristotle, Ptolemy, and Pythagoras, circa 500–400 BCE). Johannes Muller (Regiomontanus) rediscovered, translated, and published the Greek texts, bringing trigonometry to Europe in the 1400s. Georg Joachim (Rhaeticus) published highly accurate sine and cosine tables of value in the 1500s. Napier, Newton, and Leibniz all made more recent contributions. Political, social, and humanistic influences: Most of the work in trigonometry was done in the context of astronomy— that is, to predict the location of planets, it was necessary to use complex trigonometric equations. During the Renaissance, trigonometry began to be studied as a branch of mathematics of its own. An effort to further codify trigonometric values led Napier to his eventual development of logarithms, greatly simplifying the computation of values needed to solve astronomyrelated mathematics problems. Historic applications: Trigonometry has been used to solve a myriad of problems— many related to astronomy and the prediction of planetary paths. One historic application: trigonometric ratios (sine, cosine, tangent, etc.) are used to solve right triangles. One can use a variety of equations to solve problems involving right triangles and unknown quantities they may contain.For example, to find the height of the Acropolis, x, one can use the length of its shadow. Simply measure the angle formed from the base of the shadow to the top of the Acroplois, and trigonometry allows us to solve for the corresponding height of the Acropolis. Tan A = x/d (and we know both tan A, and d, so can solve for x).Number Systems Irrational Numbers Algebra Systems of Equations Geometry Parallel LInes Calculus Integrals Discrete Mathematic s Probability/ Statistics Measureme nt Combinations Correlation Coefficent Time
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