Trigonometric Identities I. Pythagorean Identities A. [pic] B. [pic] C. [pic] II. Sum and Difference of Angles Identities A. [pic] B. [pic] C. [pic] D. [pic] E. [pic] F. [pic] III. Double Angle Identities A. [pic] B. [pic] =[pic] =[pic] C. [pic] IV. Half Angle Identities A. [pic] B. [pic] C. [pic] 6-1 Inverse Trig Functions p. 468: 1-31 odd I. Inverse Trig Functions A. [pic]
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asked to find any one of the three variable quantities‚ provided the other two. A square root function that models tsunami velocity as a function of water depth is v = (gD)1/2‚ where g = 9.8m/s2 and D = water depth. Alternatively‚ this can be a quadratic model to find the depth of water if the wave velocity is known: D = v2 / g (Abbott‚ 2004‚ Banks‚ 1998). The energy of a water wave‚ particularly a tsunami‚ can be modeled as a function of wave height
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Assignment 4: Real World Quadratic Functions MAT222: Intermediate Algebra Professor Andrea Grych Assignment 4: Real World Quadratic Functions Managers and business people use quadratic equations on a daily basis in order to find out how much of a profit can be made. The following problem is an example of that. On page number 666 of the textbook‚ problem number 56 (Dugopolski‚ 2012) states that in order to get maximum profits‚ a chain store manager has been told by the main office
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pangit you CHAPTER 6: INVERSE CIRCULAR FUNCTIONS AND TRIGONOMETRIC EQUATIONS 1. INVERSE CIRCULAR FUNCTIONS • Horizontal Line Test o Any horizontal line will intersect the graph of a one-to-one function in at most one point • Inverse Function o The inverse function of the one-to-one function [pic] is defined as [pic] • Summary of Inverse Functions 1. In a one-to-one function‚ each x-value corresponds to only one y-value and
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1.1 SOLUTIONS Notes: The key exercises are 7 (or 11 or 12)‚ 19–22‚ and 25. For brevity‚ the symbols R1‚ R2‚…‚ stand for row 1 (or equation 1)‚ row 2 (or equation 2)‚ and so on. Additional notes are at the end of the section. 1. x1 + 5 x2 = 7 −2 x1 − 7 x2 = −5 1 −2 5 −7 7 −5 x1 + 5 x2 = 7 Replace R2 by R2 + (2)R1 and obtain: 3x2 = 9 x1 + 5 x2 = 7 x2 = 3 x1 1 0 1 0 1 0 5 3 5 1 0 1 7 9 7 3 −8 3 Scale R2 by 1/3: Replace R1 by R1
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questions. Time allowed : 60 minutes. There are 3 sections: 15 questions in section I‚ 15 in section II and 20 in section III. Section – I (Mental Ability) : Sets‚ Relations and Functions‚ Mathematical Induction‚ Logarithms‚ Complex Numbers & Quadratic Equations‚ Linear Inequations‚ Differentiation‚ Sequences and Series (A.P. & G.P. Misc.)‚ Trigonometry‚ Cartesian System of Rectangular Coordinates‚ Straight Lines and Family of Straight Lines‚ Circles‚ Conic Section‚ Trigonometry‚ Permutations and
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What happens to the R2? What is the adjusted R2 and why is it necessary? The formula for the R2adj will be on the exam. How do you interpret the adjusted R2? • What is a quadratic term? When should you add a quadratic term to the model? Know how to interpret the estimated coefficients to a quadratic term. • What is an interaction term? When should you add an interactive term to the model? Know how to interpret the estimated coefficients to an interactive term. • What are dummy variables
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October 12‚2015 students across the country were out of school for Columbus Day ‚ but why ? Christopher Columbus was responsible for a genocide and many other innocent deaths ‚he did not discover America ;so why ? Why do we celebrate people like him when we should actually celebrate people who had an actual positive legit impact on our lives. Born muslim in c. 780‚Al-Khwārizmī‚ became a mathematician‚not any mathematician but “the father Of Algebra “ who also studied astronomy‚geography ‚history
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Essay #1: History The history of ancient Babylonia is really long‚ but this essay is a short and to the point summery of the entire history. The history of Babylonia started near the end of the year 2000 BC‚ when invaders were attacking the Sumer kingdom. Sumer was a powerful kingdom in the western part of Asia‚ and it some what occupied what would become Babylonia. After the kingdom of Sumer was destroyed the city-states of Larsa and Isin came into settle on the land once occupied by Sumer. This
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There are many ancient civilizations that are worthy enough to be considered exceptional‚ however‚ Ancient Greece‚ without a doubt‚ is one of the most impressive ancient civilizations. What makes Ancient Greece so impressive is it’s abundant number of achievements; such as founding democracy‚ developing the world’s first libraries‚ creating the Olympic Games‚ achieving beautiful architectural feats and spitting out mathematical and scientific discoveries like no other civilization before‚ just to
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