The Ancient Greeks contributed a lot to modern society‚ but the biggest contribution of them was their contributions to the field of science and mathematics. To start off‚ the Pythagorean theorem contributed a lot to the field of mathematics. What the Pythagorean theorem does is help us to calculate the lengths of the sides of right triangles. Secondly‚ Archimedes contributed a ton to both fields. One of the most famous things that Archimedes did was find out if a crown that the king had ordered
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Pythagoras is commonly known for his discovery of the “Pythagorean Theorem”. The Pythagorean thereom states that the‚ “Square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides: c2 = a2 + b2” (Pyhtagorean…). Without Pythagoreas or his invention we would not
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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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Lesson 1: Trigonometric Functions of an Acute Angle c a b C A B The ratios of the lengths of the sides of a right triangle are called the trigonometric ratios. For convenience‚ we will name the three sides and three vertices of the right triangle as‚ a‚ b‚ and c for sides and the A‚ B‚ and C for the vertices as shown in the figure: Sine (sin) Function of an acute angle of a right triangle is equal to the ratio of the length of the opposite leg to the length of the hypotenuse. Cosine (cos)
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figures. 9. Construct formal‚ logical arguments‚ proofs‚ and constructions. 10. Determine how changes in dimensions affect the perimeter‚ area‚ and volume of common geometric figures and solids. 11. State the Pythagorean Theorem and its converse. 12. Solve problems using the Pythagorean Theorem and its converse‚ and the properties of complementary‚ supplementary‚ vertical‚ and exterior angles. 13. Define the properties of complementary‚ supplementary‚ vertical‚ and exterior angles. 14. Compute the
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in the universe. As a rule it assumes the guise of harmony in the universe‚ of lawful government in a state‚ and of a sensible way of life in the home. It brings together and unites." - The Pythagoreans Every school student
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The ancient Greek civilization had many contributions that helped explain its significance in history. During the Archaic Age‚ there were many economies and cultures. One economy were the coins. Although‚ the Greeks did not invent coins they did use coins to their advantage. They improved the design of the coins and the circulation of them. The Greeks added stamps to both sides of the coins for identification and made them of silver (Dutton 48). The Greeks used the coins for “collection of taxes
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Hardy J. E. Littlewood | Known for | Landau–Ramanujan constant Mock theta functions Ramanujan conjecture Ramanujan prime Ramanujan–Soldner constant Ramanujan theta function Ramanujan’s sum Rogers–Ramanujan identities Ramanujan’s master theorem | Influences | G. H. Hardy | HISTORY OF SRINIVASA RAMANUJAN : Srinivasa Ramanujan (22 December 1887 – 26 April 1920) was an Indian mathematician and autodidact who‚ with almost no formal training in pure mathematics‚ made extraordinary contributions
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Week One Discussion Questions Compare and contrast a relation and a function. How can you determine when a relation is a function? * -A relation is a set of ordered pairs and a function is the relation of the first component of a pair to the second component of the same pair. * -A relation is a function when a domain value of X only maps to one range value of Y. * Explain how to determine the domain and range of a function. * -A set of ordered pairs have a first component which
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After choosing a topic randomly‚ students will have 5 minutes to prepare before presenting their explanation for 5 minutes. 1. State the definition of the limit and explain the requirements for a limit to exist. Also‚ explain the 3 main techniques to evaluate limits. (Keywords: limit‚ intend‚ left‚ right‚ general‚ notation‚ 3 requirements‚ NAG‚ table‚ diagrams‚ indeterminate form‚ conjugate‚ factoring‚ substitution) The limit of the function is the height that the function intends to reach
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