Free Essay

Trigonometry Reviewer 1

In:

Submitted By pranklenjan
Words 718
Pages 3
Trigonometry (1st Grading Period)

Angles and Measures • Angle – is formed by two rays with a common endpoint. • Standard Position: An angle inscribed in a circle whose center is at the origin is said to be in “standard position” if one of the sides of the angle coincides with the positive ray of the x-axis. • Stationary Ray – “Initial Side” of the angle (the x-axis, abscissa side; the one that is NOT MOVING; the starting point of every angle) • Rotating Ray – “Terminal Side” of the angle (the one that MOVES, “rotates.”) • Angle Directions – o Counter – clockwise: POSITIVE (+) o Clockwise: NEGATIVE (−) o Quadrantal Angle: the terminal side (rotating ray) is in the coordinate system, which means that all the points in the rotating ray is not located in any of the four quadrants. The measurement of the angle is divisible by 90°. It can be positive (+) or negative (−), depending on the direction of the rotating ray.
Degrees and Radians • Degree/s – the measurement or location • Radian/s – the distance; unit of measurement is “rad” • Conversions: o Degree to Radian: ▪ deg × π . 180 o Radian to Degree: ▪ rad × 180. π
Coterminal and Reference Angles • Coterminal Angle – differs by an integral number of revolution/s; characteristic of revolutions. It is the spiral (for more than 1 revolution) that we see in the graph of the angle. It is an angle in which the terminal side coincides with another angle. • Reference Angle – the “positive acute angle” between the x-axis and the co-terminal side (rotating ray) of the given angle. It is “ALWAYS POSITIVE.” o Guide Formulas per Quadrant: ▪ Positive Angle (Counter – clockwise) • Quadrant I: 180(0) + θ • Quadrant II: 180(1) − θ • Quadrant III: 180(1) + θ • Quadrant IV: 180(2) − θ ▪ Negative Angle (Clockwise) • Quadrant IV: 180(0) − θ • Quadrant III: 180(-1) + θ • Quadrant II: 180(-1) − θ • Quadrant I: 180(-2) + θ

The Unit Circle • Unit = 1 • Arc Length – the distance between two points along the circle. (radiant measure) • The entire Unit Circle is = 2π o Formula: 2π × 1/n = d ▪ n – the number of equal divisions around the unit circle. ▪ d – the distance of two consecutive points.
Points on the Unit Circle • Abscissa – x-axis • Ordinate – y-axis • Use the Pythagorean Theorem in finding the coordinates of a point on the Unit Circle. o 12 = x2 + y2 • The arrangement of coordinates of point: ( x , y )
Sine and Cosine Functions • Cosine: The “x-axis” (abscissa) • Sine: The “y-axis” (ordinate) • The Special Right Triangles: o 30° – 60° – 90° and 60° – 30° – 90° Triangles: ▪ 30° (√3/2 , ½) ▪ 60° (½ , √3/2) ▪ 90° (0 , 1) o 45° – 45° – 90° Triangle: ▪ 45° (√2/2, √2/2) ▪ 90° (0 , 1) • If the degree-angle is not part of the Special Right Triangles: Use the CALCULATOR ( o RMINDER: Round-off to the nearest 4th decimal place. • If in radiant form: CONVERT FIRST TO DEGREE, THEN SOLVE.
Graph of Sine Function • y = a sin b θ o a: changes the amplitude, max. point, and the min. point of the wave; Simply the “wave height.” o b: changes the cycles in a period, and the intercepts; Simply the “wave length.” o Both a and b = 1 if there is no integer indicated in the function. • Components: o Amptitude (a): The “highest point” in the graph. It is the numerical coefficient of “sine (sin)” in the equation. It is the “MAXIMUM LIMIT” of the wave height. o Period = 2π: Simply, “A period is found in every 2π.” It can’t be determined unless the graph is shown. ▪ Formula: • k = n 2π • k – the limit given in the domain (abscissa, x-axis) • n – the number of periods

o Cycle: A complete wave, which starts from the base point of the abscissa (0), passes through the maximum point, then passes through the base point of the abscissa (0) again, then goes down and passes through the minimum point, and finally goes back to the base point of the abscissa (0). o Intercepts: The points located along the x-axis; points where the wave intercepts the x-axis. o Maximum Point: “Coordinate of the highest point” that the wave passes through in the graph. o Minimum Point: “Coordinate of the lowest point” that the wave passes through in the graph.

Reference: • My Notes ( • And My Stock Knowledge (((

Similar Documents

Free Essay

Math Algebra

...MAPÚA INSTITUTE OF TECHNOLOGY Department of Mathematics COURSE SYLLABUS 1. Course Code: Math 10-3 2. Course Title: Algebra 3. Pre-requisite: none 4. Co-requisite: none 5. Credit: 3 units 6. Course Description: This course covers discussions on a wide range of topics necessary to meet the demands of college mathematics. The course discussion starts with an introductory set theories then progresses to cover the following topics: the real number system, algebraic expressions, rational expressions, rational exponents and radicals, linear and quadratic equations and their applications, inequalities, and ratio, proportion and variations. 7. Student Outcomes and Relationship to Program Educational Objectives Student Outcomes Program Educational Objectives 1 2 (a) an ability to apply knowledge of mathematics, science, and engineering √ (b) an ability to design and conduct experiments, as well as to analyze and interpret from data √ (c) an ability to design a system, component, or process to meet desired needs √ (d) an ability to function on multidisciplinary teams √ √ (e) an ability to identify, formulate, and solve engineering problems √ (f) an understanding of professional and ethical responsibility √ (g) an ability to communicate effectively √ √ (h) the broad education necessary to understand the impact of engineering solutions in the global and societal context √ √ (i) a recognition of the need for, and an ability to engage...

Words: 1522 - Pages: 7

Premium Essay

Study Habits and Its Effect to Academic Performance

...Chapter I INTRODUCTION Background of the Study Our character is a collection of our habits, and habits have a powerful role in our lives. Habits consist of knowledge, skill, and desire. Knowledge allows us to know what to do, skill gives us the ability to know how to do it, and desire is the motivation to do a certaintask (Covey, 1990). Habits are routines of behaviour that are repeated regularly and tend to occur subconsciously. Habitual behaviour often goes unnoticed in persons exhibiting it, because a person does not need to engage in self-analysis when undertaking routine tasks. Study skills include how a person studies, as well as the particular resources a person uses. They are intentional use of one or more cognitive processes to accomplish a particular task. Good study skills include note-taking, reading, summarizing, organizing, identifying important information, and meaningful learning and elaboration (Ormrod, 2008).They are generally critical to success in school, are considered essential for acquiring good grades, and are useful for learning throughout one's life. Study skills are the methods of researching and learning that are used to absorb educational information. It has been widely accepted in modern times that college is a time to learn, experiment, and grow. Academic performance is the commonly used gauge with which to determine whether or not a student has indeed learned what he has been taught. It is the ability of the student to apply academic...

Words: 5295 - Pages: 22

Premium Essay

Performance of the Criminology Graduates in the Board Examination: in Relation to Enhancement Program

...CHAPTER I The Problem and Its Background Introduction Education is instrumental in harnessing man’s potentials and capacities to make him a productive and effective member of society; hence the total development of the individual is the ultimate aim of education. Thus, schools were established in all feasible areas to quench man’s quest for further knowledge and optimum development. In effect, awareness to the significant benefits of education directed the school towards offering different courses, specifically in the tertiary level. One of such education is Criminology, a highly intellectual field, especially because the majority of the job’s responsibilities rely on determining and analyzing criminal patterns. According to Agas (2008), criminology focused on the study of crime, the causes of crime, the meaning of crime in terms of law, and community reaction to crime. It also deals with the scientific study of criminals and criminal behavior. Criminologists attempt to build theories that explain why crimes occur and test those theories by observing behavior. This course focuses on such topics as criminal jurisprudence, criminal sociology, crime detection and investigation, drug education and vice control, law enforcement administration, correctional administration, industrial security management, probation, and juvenile delinquency. As such, criminology students shall pass all of the General Education and Professional subjects and undergo Comprehensive Review...

Words: 9482 - Pages: 38

Premium Essay

Case

...Killer Cover Letters & Resumes! WetFeet Insider Guide by Rosanne Lurie The WetFeet Research Methodology You hold in your hands a copy of the best-quality research available for job seekers. We have designed this Insider Guide to save you time doing your job research and to provide highly accurate information written precisely for the needs of the job-seeking public. (We also hope that you’ll enjoy reading it, because, believe it or not, the job search doesn’t have to be a pain in the neck.) Each WetFeet Insider Guide represents hundreds of hours of careful research and writing. We start with a review of the public information available. (Our writers are also experts in reading between the lines.) We augment this information with dozens of in-depth interviews of people who actually work for each company or industry we cover. And, although we keep the identity of the rank-and-file employees anonymous to encourage candor, we also interview the company’s recruiting staff extensively, to make sure that we give you, the reader, accurate information about recruiting, process, compensation, hiring targets, and so on. (WetFeet retains all editorial control of the product.) We also regularly survey our members and customers to learn about their experiences in the recruiting process. Finally, each Insider Guide goes through an editorial review and fact-checking process to make sure that the information and writing live up to our exacting standards before it goes out the door. Are...

Words: 21838 - Pages: 88

Premium Essay

File Sharing - Case Study

...sharing as a reliable source of their studies. Also, to make them know all possibilities wherein they can use file sharing in a good way. * To the instructors: * To inform them how east learning process could be, for both instructors and students, through the use of file sharing. * To the parents: * To inform them that internet, through the use of file sharing, is a wide resource of information which can help their children with their studies. * To the out of school youth: * To educate them that education can also exist outside the school. For them to have knowledge that through the internet, they can still learn many things that will uplift their mental capacity. Webpage Codes HTML folder contents: * * 1.html * 2.html * A.html * B.html * C.html *...

Words: 7679 - Pages: 31

Premium Essay

Comps

...10 Qualitative Research Methods in Psychology Deborah Biggerstaff Warwick Medical School University of Warwick, Coventry UK 1. Introduction In the scientific community, and particularly in psychology and health, there has been an active and ongoing debate on the relative merits of adopting either quantitative or qualitative methods, especially when researching into human behaviour (Bowling, 2009; Oakley, 2000; Smith, 1995a, 1995b; Smith, 1998). In part, this debate formed a component of the development in the 1970s of our thinking about science. Andrew Pickering has described this movement as the “sociology of scientific knowledge” (SSK), where our scientific understanding, developing scientific ‘products’ and ‘know-how’, became identified as forming components in a wider engagement with society’s environmental and social context (Pickering, 1992, pp. 1). Since that time, the debate has continued so that today there is an increasing acceptance of the use of qualitative methods in the social sciences (Denzin & Lincoln, 2000; Morse, 1994; Punch, 2011; Robson, 2011) and health sciences (Bowling, 2009; Greenhalgh & Hurwitz, 1998; Murphy & Dingwall, 1998). The utility of qualitative methods has also been recognised in psychology. As Nollaig Frost (2011) observes, authors such as Carla Willig and Wendy Stainton Rogers consider qualitative psychology is much more accepted today and that it has moved from “the margins to the mainstream in psychology in the UK.” (Willig & Stainton...

Words: 16075 - Pages: 65

Free Essay

K-12 Math Curriculum

...The Changing Mathematics Curriculum: An Annotated Bibliography Third Edition April 2005 1 2 The K–12 Mathematics Curriculum Center The K–12 Mathematics Curriculum Center (K–12 MCC) supports school districts as they build effective mathematics education programs using curricula that align with the National Council of Teachers of Mathematics’ (NCTM) Curriculum and Evaluation Standards for School Mathematics (1989) and Principles and Standards for School Mathematics (2000). The K–12 MCC offers a variety of products and services to assist mathematics teachers and administrators. Our seminars address selecting and implementing new curricula, designing professional development and support, aligning curriculum with assessment, and examining leadership in curricular change. Our other resources include: About This Publication This publication, an annotated bibliography of articles relevant to Standards-based mathematics curriculum reform, is intended as a resource for educators and communities considering the selection and implementation of a Standards-based mathematics curriculum. It also may assist individuals who are interested in learning about the student achievement, classroom practices, and implementation challenges associated with the use of Standards-based materials. When gathering resources for this publication, the K–12 Mathematics Curriculum Center staff reviewed articles that either addressed important issues in mathematics curriculum change or shared experiences...

Words: 26387 - Pages: 106

Free Essay

Computer Vision

...Learning OpenCV Gary Bradski and Adrian Kaehler Beijing · Cambridge · Farnham · Köln · Sebastopol · Taipei · Tokyo Learning OpenCV by Gary Bradski and Adrian Kaehler Copyright © 2008 Gary Bradski and Adrian Kaehler. All rights reserved. Printed in the United States of America. Published by O’Reilly Media, Inc., 1005 Gravenstein Highway North, Sebastopol, CA 95472. O’Reilly books may be purchased for educational, business, or sales promotional use. Online editions are also available for most titles (safari.oreilly.com). For more information, contact our corporate/institutional sales department: (800) 998-9938 or corporate@oreilly.com. Editor: Mike Loukides Production Editor: Rachel Monaghan Production Services: Newgen Publishing and Data Services Cover Designer: Karen Montgomery Interior Designer: David Futato Illustrator: Robert Romano Printing History: September 2008: First Edition. Nutshell Handbook, the Nutshell Handbook logo, and the O’Reilly logo are registered trademarks of O’Reilly Media, Inc. Learning OpenCV, the image of a giant peacock moth, and related trade dress are trademarks of O’Reilly Media, Inc. Many of the designations used by manufacturers and sellers to distinguish their products are claimed as trademarks. Where those designations appear in this book, and O’Reilly Media, Inc. was aware of a trademark claim, the designations have been printed in caps or initial caps. While every precaution has been taken in the preparation of this...

Words: 150684 - Pages: 603

Free Essay

Reflection Paper About Precious

...(NiZn) Germanium Glass Ice Mica Neoprene Nylon Paper Plexiglas Polyethylene Polypropylene Polystyrene Porcelain (dry process) Pyranol Pyrex glass Quartz (fused) Rubber Silica or SiO2 (fused) Silicon Snow Sodium chloride Soil (dry) Steatite Styrofoam Teflon Titanium dioxide Water (distilled) Water (sea) Water (dehydrated) Wood (dry) � r �� / � 1.0005 25 8.8 2.7 4.74 1200 1.001 12.4 16 4–7 4.2 5.4 6.6 3.5 3 3.45 2.26 2.25 2.56 6 4.4 4 3.8 2.5–3 3.8 11.8 3.3 5.9 2.8 5.8 1.03 2.1 100 80 1 1.5–4 0.1 0.000 6 0.002 0.022 0.013 0.000 25 0.002 0.05 0.000 6 0.011 0.02 0.008 0.03 0.000 2 0.000 3 0.000 05 0.014 0.000 5 0.000 6 0.000 75 0.002 0.000 75 0.5 0.000 1 0.05 0.003 0.000 1 0.000 3 0.001 5 0.04 4 0 0.01 Conductivity (� ) Material Silver Copper Gold Aluminum Tungsten Zinc Brass Nickel Iron Phosphor bronze Solder Carbon steel German silver Manganin Constantan Germanium Stainless steel , S/m 6.17 × 107 4.10 × 107 3.82 × 107 1.82 × 107 1.67 × 107 1.5 × 107 1.45 × 107 1.03 × 107 1 × 107 0.7 × 107 0.6 × 107 0.3 × 107 0.227 × 107 0.226 × 107 0.22 × 107 0.11 × 107 5.80 × 107 Material Nichrome Graphite Silicon Ferrite (typical) Water (sea) Limestone Clay Water (fresh) Water (distilled) Soil (sandy) Granite Marble Bakelite Porcelain (dry process) Diamond Polystyrene Quartz , S/m 0.1 × 107 7 × 104 2300 100 5 10−2 5 × 10−3 10−3 10−4 10−5 10−6 10−8 10−9 10−10 2 ×...

Words: 177667 - Pages: 711

Premium Essay

Hiiiiiiiiiiiiii

...mol21 5.29310211 m BEST KNOWN VALUE* 299 792 458 m/s (exact) 1.602 176 4871402 310219 C 9.109 382 151452 310231 kg 1.672 621 6371832 310227 kg 6.674 281672 310211 N # m2/kg 2 4p31027 (exact) 1/m0c2 (exact) 1.380 65041242 310223 J/K 8.314 4721152 J/K # mol 5.670 4001402 31028 W/m2 # K4 6.626 068 961332 310234 J # s 6.022 141 791302 31023 mol21 5.291 772 08591362 310211 m *Parentheses indicate uncertainties in last decimal places. Source: U.S. National Institute of Standards and Technology, 2007 values SI PREFIXES POWER 1024 1021 1018 1015 1012 109 106 103 102 101 100 1021 1022 1023 1026 1029 10212 10215 10218 10221 10224 THE GREEK ALPHABET PREFIX yotta zetta exa peta tera giga mega kilo hecto deca — deci centi milli micro nano pico femto atto zepto yocto SYMBOL Y Z E P T G M k h da — d c m μ n p f a z y Alpha Beta Gamma Delta Epsilon Zeta Eta Theta Iota Kappa Lambda Mu Nu Xi Omicron Pi Rho Sigma Tau Upsilon Phi Chi Psi Omega UPPERCASE A B G D E Z H U I K L M N J O P R S T Y F X C V LOWERCASE a b g d P z h u i k l m n j o p r s t y f x c v Conversion Factors (more conversion factors in Appendix C) Length 1 in 5 2.54...

Words: 201181 - Pages: 805

Free Essay

Organization

...into any information retrieval system, electronic or mechanical, without the written permission of the copyright owner. All inquiries should be addressed to: Barron's Educational Series, Inc. 250 Wireless Boulevard Hauppauge, NY 11788 http://www.barronseduc.com Library of Congress Catalog Card No. 00-030344 International Standard Book Number 0-7641-1365-8 Library of Congress Cataloging-in-Publication Data Bromberg, Murray. 1100 words you need to know / Murray Bromberg, Melvin Gordon. p. cm. Includes index. ISBN 0-7641-1365-8 1. Vocabulary. I. Title: Eleven hundred words you need to know. II. Gordon, Melvin. III. Title. PE1449.B643 2000 428.1dc21 00-030344 PRINTED IN THE UNITED STATES OF AMERICA 987654321 < previous page page_ii next page > < previous page page_iii next page > Page iii Contents Full Pronunciation Key Weeks 146 Buried Words Words in Context Analogy Review Answers Final Review Test The Panorama of Words Index iv 1 299 303...

Words: 125626 - Pages: 503

Premium Essay

Heuy2Kj4

...Pennsylvania State University Julia Lobur Pennsylvania State University World Headquarters Jones and Bartlett Publishers 40 Tall Pine Drive Sudbury, MA 01776 978-443-5000 info@jbpub.com www.jbpub.com Jones and Bartlett Publishers Canada 2406 Nikanna Road Mississauga, ON L5C 2W6 CANADA Jones and Bartlett Publishers International Barb House, Barb Mews London W6 7PA UK Copyright © 2003 by Jones and Bartlett Publishers, Inc. Cover image © David Buffington / Getty Images Illustrations based upon and drawn from art provided by Julia Lobur Library of Congress Cataloging-in-Publication Data Null, Linda. The essentials of computer organization and architecture / Linda Null, Julia Lobur. p. cm. ISBN 0-7637-0444-X 1. Computer organization. 2. Computer architecture. I. Lobur, Julia. II. Title. QA76.9.C643 N85 2003 004.2’2—dc21 2002040576 All rights reserved. No part of the material protected by this copyright notice may be reproduced or utilized in any form, electronic or mechanical, including photocopying, recording, or any information storage or retrieval system, without written permission from the copyright owner. Chief Executive Officer: Clayton Jones Chief Operating Officer: Don W. Jones, Jr. Executive V.P. and Publisher: Robert W. Holland, Jr. V.P., Design and Production: Anne Spencer V.P., Manufacturing and Inventory Control: Therese Bräuer Director, Sales and Marketing: William Kane Editor-in-Chief, College: J. Michael Stranz Production...

Words: 118595 - Pages: 475

Free Essay

If I Stay

...Registered Offices: 80 Strand, London WC2R 0RL, England This book is a work of fiction. Names, characters, places, and incidents are either the product of the author’s imagination or are used fictitiously, and any resemblance to actual persons, living or dead, business establishments, events, or locales is entirely coincidental. Copyright © 2009 by Gayle Forman “Waiting for Vengeance” © by Oswald Five-0, Serenade , Grinning Idiot Records. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system now known or to be invented, without permission in writing from the publisher, except by a reviewer who wishes to quote brief passages in connection with a review written for inclusion in a magazine, newspaper, or...

Words: 51106 - Pages: 205