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Math factor PDF

246 Pages·1996·16.2 MB·English
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_±ni-fvucz w Lesson 1: Radian Measurement Student Workbook Produced by for Liberia EDUCATION This guide accompanies Radian Measurement from the Math Factor series. Writer: Wendy Stanhope Editor: Wilma Gonsalves Producer: Katherine Rankin Educators in public educational institutions in Alberta may verbally quote, or use in exams, excerpts from this publication, except material that has been credited to another source. Additional copies of the guide can be obtained, at cost plus handling and postage, from the ACCESS Media Resource Centre. When ordering videotapes, please use the Basic Program Number (BPN), plus the program number and title (s). In addition, please attach a p urchase order to cover duplication fees. The order number and title is BPN #3689-09 Trigonometric and Circular Functions: Radian Measurement For information about other ACCESS materials, the toll-free number for Alberta educators is 1-800-352-8293, or you may write to the following address: ACCESS Media Resource Centre 3720 - 7 6 Avenue EDMONTON, Alberta T6B 2N9 Telephone: (403) 440-7729 Fax: (403) 440-8899 inquiries from outside Alberta regarding purchase of this series or other ACCESS materials should be directed to ACCESS Program Sales at the address given above. © 1996 Alberta Education ISBN 1-896762-06-9 PRINTED AND BOUND IN CANADA UNIVERSITY LIBRARY UNIVERSITY OF ALBERTA MATH FACTOR TRIGONOMETRIC AND Lesson 1: RADIAN MEASUREMENT LEARNER EXPECTATIONS By the end of Lesson 1 y ou should be able to: define the radian measurement of a c entral angle in a c ircle use the formula G = j t o solve for 6, a o r r convert angle measurements between degree and radian measure and vice versa apply this knowledge to solving problems involving sector area and angular velocity y This lesson has four parts: Defining One Radian Converting EXPLANATION OF ICONS Building Blocks: Do you remember most of y our Mathematics 20? This course builds upon many of those skills and concepts. The Building Blocks icon appears in the workbook to indicate review examples and/or exercises. To refresh your memory, do this section in the workbook before watching the video. Video: Whenever this icon appears in the workbook, you should watch the indicated segment of the video program. Preceding this icon, there is often a p roblem titled “Challenge yourself.” Try the problem before watching the video. As you work through a p rogram segment, stop the video to • challenge yourself to find the solution before it is g iven • write down key ideas and examples • reflea on what is being taught Challenge Yourself: This icon sometimes appears on the television screen when a n ew example is starting. When it appears, it i s suggested that you stop the video and try the example yourself before proceeding. For your convenience, sometimes the example is already written in the workbook. The solution will be given in the video. Student Workbook: This icon appears on the television screen at the end of teaching segments, when a new skill or sub-skill has been taught The icon indicates that the workbook contains related examples and/or exercises. Stop the video to study the examples and complete the exercises. The video icon in the workbook will indicate when you should return to the video and move on to learning a n ew skill. Excellence: This icon appears in the workbook to indicate advanced level examples or exercises that you might find challenging. Test your new skills! Textbook Reference: This icon appears in the workbook to indicate additional examples and exercises that can be found in the following three textbooks: • M athematics 12 (Addison- Wesley) • M athematics: Principles and Process 12 (Nelson Canada) • H oltmath 12 (Holt, Rinehart and Winston oj Canada, Limited) 0 TRIGONOMETRIC AND CIRCULAR FUNCTIONS Additional Examples Mathematics 12: pp. 198, 199 Mathematics: Principles and Process 12: p. 181 Holtmath 12: p. 287 Exercises 1 . Cut off a p iece of string that is equal in length to the radius of this circle. Use this string to draw an angle of one radian. 2. Using the string as a m easuring tool, how many lengths of string are there around the circle's circumference? Approximately how many radians are there in 360°? 3. Complete the following definition. An angle of one radian is defined as following symbols represents in the formula. a. 9 b. a c. r of 5 r ad? 4 . In general , radians can be defined by the formula 9- j. Explain what each of the 5 . If t he radius of a c ircle is 7 c m, then what is the measur e of the arc length for an angle TRIGONOMETRIC AND CIRCULAR FUNCTIONS Radian Measurement the radian measure of this central angle? 6. The central angle of a c ircle of radius 10 cm subtends an arc length of 45 cm. What is radian measure of this central angle? central angle that subtends an arc length of 2kt1 7. The cen tral angle of a c ircle of radius r c m subtends an arc length of 2k r. What is the 2k rad? ^ EX ERCISE la SOLUTIONS are at the back of this workbook. 8 .A c ircle of radius r h as a c ircumference of 2kt. What is the degree measure of the 9 .Compare y our answers in q uestions 7 a nd 8. What degree measure is equivalent to TRIGONOMETRIC AND CIRCULAR FUNCTIONS Example 1 Convert 60° to radian measure. Solution Method 1 180° = /rrad To convert degrees to radians, multiply \ rad 1° = 180 the number of degrees by 755- . r \ n rad 60° =60° = — r ad v# 3 Method 2 180' n _ n # Make equivalent ratios of radians to 180° 60° degrees: —k = Hn uummbbeerr ooff d rladgirarnes 0_r_ 180° n- 60° k using you can compare degrees to radians. n 3 Exact Radian 1 8M0e°a sure § i s the exact radian equivalent for 60°. Approximate Radian Measure o To express radians in decimal form, replace n b y 3.14... by using the k . 3.14 3 k button on your calculator. = 1 .05 rad 60" TRIGONOMETRIC AND CIRCULAR FUNCTIONS Radian Measurement Example 2 Convert jn rad to degree measure. Solution /rrad = 1 80° To convert exact radians to degrees, replace n rad by 180c f*rad = f( l80‘) Exampl=e 1 3 53° Convert 3.66 rad to degree measure. Solution Method 1 To convert decimal equivalent K 1 rad = 1 801 radians to degree measure, multiply/ 3.66 rad = 3 .66 If 1 2 0* 1 . J the number of radians by , * where n = 3 .14... . Method 2 = 2 10° smmss 1 ' - Make equivalent ratios of degrees to degrees — ► 180° n draedgiraeness radians — ► n 3.66 ^ \ radians or radians to degrees. ‘ § ' • . ' 180° (3.66) = n n 180 ° ( 3.6 6) = n [ Solve for n. K 180 ° ( 3.6 6) = n f Using the n b utton on a c alculator, 3.14 L k = 3 .14.... A n = 2 10° Additional Examples Mathematics 12: p. 200 (Question 3) Mathematics : P rinciples and Process 12: pp. 181, 182 Holtmath 12: p. 287 0 TRIGONOMETRIC AND CIRCULAR FUNCTIONS Radian Measurement Exercises 10. Complete the following table. Exact Radian Approximate Radian Degrees Measure Measure 7T 2 K 3.14 it 2k 0° 6.28 270° 6 5.76 5 i t T 225° 1 1 . Certain angles are identified on each of the following circles. Convert the measure of the identified angles from degree to exact radian measure. a. quadrant angles b. angles with a r eference angle of 45° ra TRIGONOMETRIC AND CIRCULAR FUNCTIONS Radian Measurement c. angles with a reference angle of 30° d. angles with a r eference angle of 60° ^ EX ERCISE lb SOLUTIONS are at the back of t his workbook. Additional Practice Mathematics 12\ p. 200 (Question 1), p. 201 (Questions 2-4) Mathematics: Principles and Process 12\ p. 182 (Questions 1, 2, 5), p. 183 (Question 9) Holtniath 12: p. 287 (Questions 3, 4)

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