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UNIVERSITY OF THE PHILIPPINES (LOS BAÑOS) MATH 17 - COLLEGE ALGEBRA AND TRIGONOMETRY Supplementary Exercise
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UNIVERSITY OF THE PHILIPPINES (LOS BAÑOS)
MATH 17 - COLLEGE ALGEBRA AND TRIGONOMETRY
Supplementary Exercise
Supp exer 15
UNIVERSITY OF THE PHILIPPINES (LOS BAÑOS)
MATH 17 - COLLEGE ALGEBRA AND TRIGONOMETRY
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Exercie 12 (take home)
This document contains instructions for a take-home math exercise assigned to be completed and turned in on Wednesday November 23rd. The exercise includes 4 problems: 1) finding the fundamental solution set of 4 equations, 2) finding the solution set of 2 other equations and checking the solutions, 3) solving a triangle with given side lengths, and 4) calculating the distance to a boat given the angle of depression and height of a lighthouse.
Supp exer 17
This document contains mathematics exercises involving trigonometric functions and identities. It asks the student to 1) find the values of trig functions given angle measures, 2) prove various trigonometric identities, and 3) use half-angle identities to find trig functions of divided angles given the functions of the original angles.
Supp exer 18
UNIVERSITY OF THE PHILIPPINES (LOS BAÑOS)
MATH 17 - COLLEGE ALGEBRA AND TRIGONOMETRY
Supplementary Exercise
Supp exer 13
UNIVERSITY OF THE PHILIPPINES (LOS BAÑOS)
MATH 17 - COLLEGE ALGEBRA AND TRIGONOMETRY
Supplementary Exercise
2.1 lbd numbers and their practical applications
The document discusses the history and development of numbers and numerical systems. It begins with early counting methods using tallies and evolved to include the Egyptian, Babylonian, Roman, and Hindu-Arabic systems. The modern number system is then built up from the natural numbers to integers to rational numbers to real numbers, which include irrational numbers. Imaginary and complex numbers were later introduced to solve problems involving square roots of negative numbers. Place value systems and the ability to represent zero were important developments.
Chapter 1 (part 3)
The document discusses common fallacies of reasoning. It aims to help readers recognize and discard errors in reasoning by describing fallacies of relevance, including subjectivism, appeal to ignorance, limited choice, appeal to emotion, appeal to force, inappropriate appeal to authority, personal attack, begging the question, and non sequitur. It also discusses fallacies involving numbers and statistics such as appeal to popularity, appeal to numbers, hasty generalization, availability error, false cause, and issues with percentages. The overall goal is to help evaluate information critically and carefully exercise reasoning.
Recommended
Supp exer 14
UNIVERSITY OF THE PHILIPPINES (LOS BAÑOS)
MATH 17 - COLLEGE ALGEBRA AND TRIGONOMETRY
Supplementary Exercise
Supp exer 15
UNIVERSITY OF THE PHILIPPINES (LOS BAÑOS)
MATH 17 - COLLEGE ALGEBRA AND TRIGONOMETRY
Supplementary Exercise
Exercie 12 (take home)
This document contains instructions for a take-home math exercise assigned to be completed and turned in on Wednesday November 23rd. The exercise includes 4 problems: 1) finding the fundamental solution set of 4 equations, 2) finding the solution set of 2 other equations and checking the solutions, 3) solving a triangle with given side lengths, and 4) calculating the distance to a boat given the angle of depression and height of a lighthouse.
Supp exer 17
This document contains mathematics exercises involving trigonometric functions and identities. It asks the student to 1) find the values of trig functions given angle measures, 2) prove various trigonometric identities, and 3) use half-angle identities to find trig functions of divided angles given the functions of the original angles.
Supp exer 18
UNIVERSITY OF THE PHILIPPINES (LOS BAÑOS)
MATH 17 - COLLEGE ALGEBRA AND TRIGONOMETRY
Supplementary Exercise
Supp exer 13
UNIVERSITY OF THE PHILIPPINES (LOS BAÑOS)
MATH 17 - COLLEGE ALGEBRA AND TRIGONOMETRY
Supplementary Exercise
2.1 lbd numbers and their practical applications
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Chapter 1 (part 3)
The document discusses common fallacies of reasoning. It aims to help readers recognize and discard errors in reasoning by describing fallacies of relevance, including subjectivism, appeal to ignorance, limited choice, appeal to emotion, appeal to force, inappropriate appeal to authority, personal attack, begging the question, and non sequitur. It also discusses fallacies involving numbers and statistics such as appeal to popularity, appeal to numbers, hasty generalization, availability error, false cause, and issues with percentages. The overall goal is to help evaluate information critically and carefully exercise reasoning.
Chapter 1 (part 4)
This document discusses the relationships between logic, mathematics, and science. It provides examples of how philosophers have used logic to explore truths, such as William Paley's argument for the existence of a creator based on biological complexity. The development of symbolic logic allowed mathematics to be treated as a logical system, as in Bertrand Russell's Principia Mathematica. However, Kurt Gödel's incompleteness theorems proved that a fully consistent and complete logical system is impossible. While logic has limitations, it remains an important tool for understanding and acquiring knowledge through the scientific method.
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This document discusses the development of the modern number system, including natural numbers, integers, rational numbers, real numbers, imaginary and complex numbers. It provides examples and definitions of these different types of numbers. The document also focuses on prime numbers, describing properties like twin primes and Mersenne primes. Methods for finding primes like the Sieve of Eratosthenes are explained. Applications of prime numbers in cryptography and factoring are also mentioned.
3.3 calculus the language of change
Calculus is the mathematical study of change. It has two main areas: differential calculus concerns slopes and rates of change, while integral calculus concerns area and volume. The foundations of calculus were established in the late 17th century by Newton and Leibniz, who recognized that differentiation and integration are inverse processes. Calculus is based on the concept of a limit, which allows approximating values that cannot be calculated directly. The document then provides an example of using limits to calculate the area under a curve by dividing it into rectangular elements and taking the sum as the number of elements approaches infinity.
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Measurements and estimations involve uncertainty that arises from imprecision, random errors, and systematic errors. Numbers can be categorized as exact or approximate, with approximations involving uncertainty. Uncertainty must be expressed either implicitly by careful rounding or explicitly using ranges. Significant digits indicate the precision of measurements and estimations, and implied uncertainty ranges can be determined from them. When combining approximate values, answers must be rounded or expressed as ranges consistent with the least precise input to properly account for accumulated uncertainties.
2.3 problem solving strategies
The document discusses strategies and techniques for solving quantitative problems. It emphasizes that problem solving requires creativity, organization, and experience. Some key points made include: keeping track of units is an important problem solving tool; no single strategy always works so flexibility is important; understanding the context and restating the problem can help clarify the solution; and the most effective problem solvers view challenges as opportunities to improve their skills through practice.
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Algebra began with ancient Egyptians and Babylonians solving linear and quadratic equations. Over time, mathematicians generalized arithmetic operations and developed symbolic notation. Modern algebra arose from studying abstract structures like groups. A group is a set with operations where elements combine associatively, every element has an inverse, and a unique identity element exists. Groups include addition modulo m and permutations. Abstract algebra studies algebraic properties of different mathematical systems.
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chapter 1 (part 2)
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Geometry began with ancient Egyptians and Babylonians using practical measurements and Pythagorean relationships in construction. Greeks like Euclid later formalized geometry, establishing five postulates including the parallel postulate. Many unsuccessfully tried to prove this postulate, leading to non-Euclidean geometries developed by Bolyai, Lobachevsky, and others. These geometries have different properties than Euclidean geometry and opened new areas of mathematical exploration. Fractal geometry, developed by Mandelbrot, describes naturally occurring structures through fractional dimensions and infinite complexity across all scales.
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Supp exer 16
- 1. EXERCISES 4.7 A. Find the exact value of the following. 1. 4. 2. 5. 3. 6. B. Find and and determine the quadrants where are. 1. and where are in QI 2. and where is in QII and is in QIV. 3. and where are in QIV 4. and where are in QIII C. Verify the following using the sum and difference identities. 1. 5. 2. 6. 3. 7. 4. 8. D. Verify the following by getting the circular function values of both sides of the equation, then applying the sum and difference identities. 1. 4. 2. 5. 3. 6. 4. E. Prove that . F. Find the solution set of the following equations. 1. 3. 2.