OER Math 1060 – Trigonometry
CHAPTER 4 TRIGONOMETRIC IDENTITIES AND FORMULAS. 166. 4.1 The Even/Odd answers. For example when fitting a sine function to the data
Sections 4.1-4.4
. Worksheet by Kuta Software LLC. -4-. Evaluate the trigonometric function using Chapter 4: Trigonometric. Functions. Sections 4.5-4.7. Page 38. © P2w0y1o9G ...
Chapter 4 Trigonometry and the Unit Circle
Chapter 4. Page 7 of 85. Section 4.1 Page 176. Question 12 a) Use a proportion with r = 9.5 and central angle 1.4 radians. arc length central angle.
Worked Examples from Introductory Physics (Algebra–Based) Vol. I
၂၀၁၂၊ အောက် ၃ 4.1.4 Units and Stuff . ... CHAPTER 4. FORCES I. F. F. Rearth. Figure 4.3: Earth exerts force F on ...
Untitled
Trigonometry (4.1-4.4). Name. Key. Chapter 4 Review Problems: Non-calculator. Find the exact value of each of the trigonometric functions given. Watch signs! 5π.
tangent – the slope ratio (trigonometry) 4.1.1
In the first section of Chapter 4 students consider different slope triangles for a given line or segment and notice that for each line
Lesson 4.1.1 - 4-6.
The slope ratio for 68°≈ 2.5 so. BC≈ 4 feet. Thus
Chapter 4 Trigonometry
Chapter 4. Trigonometry. Section 4.1 Radian and Degree Measure. Objective: In this lesson you learned how to describe an angle and to convert between radian
NEW GENERAL MATHEMATICS
• Chapter revision test answers: the answers for all the chapter revision tests are Assign questions 1 3 and 4 from Worksheet 4 as homework. Assessment.
CHAPTER 4 Trigonometry
306 Chapter 4 Trigonometry. © 2018 Cengage Learning. All Rights Reserved. Sample answers: ... Section 4.1 Radian and Degree Measure 307.
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160 Chapter 4 Trigonometric Functions. Chapter 4 Section 4.1 Angles and Their Measures ... (This would be the answer for any two adjacent lanes.).
Chapter 4 Trigonometry and the Unit Circle
MHR • 978-0-07-0738850 Pre-Calculus 12 Solutions Chapter 4 Section 4.1 Page 175 ... Joran's answer includes the given angle obtained when n = 0.
4 Trigonometric Functions
shown in FIGURE 4.1.4 CHAPTER 4 TRIGONOMETRIC FUNCTIONS ... Exercises 4.1 Answers to selected odd-numbered problems begin on page ANS–14.
Chapter 4
Precalculus with Limits Answers to Section 4.1. 1. Chapter 4. Section 4.1 (page 290) 4. radians. 5. 1 radian. 6. 6.5 radians. 7. (a) Quadrant I.
164 Chapter 4 Trigonometric Functions
4. ? radians. Quick Review 4.1. 1. C=2? 2.5=5? in. 2. C=2? 4.6=9.2? m. 3. 4. (This would be the answer for any two adjacent lanes.).
Chapter 4- Trigonometry
Chapter 4- Trigonometry 4.1 – Special Angles 1 - Worksheet ... 4. Solve the following equations for 0° ? ? 360°. Round answers to the nearest ...
OER Math 1060 – Trigonometry
CHAPTER 4 TRIGONOMETRIC IDENTITIES AND FORMULAS. 166. 4.1 The Even/Odd Identities Use your answer from part (1) to determine the radian measure for ...
Trigonometric Functions
CHAPTER 4 Trigonometric Functions. 4.1. Angles and Their Measures You may use a graphing calculator when answering these questions.
4 Trigonometry - 4.1 Squares and Triangles
Find the length of the hypotenuse of the triangle shown in the diagram. Give your answer correct to. 2 decimal places. Solution. As this is a right angled
Trigonometry worksheets and PowerPoints - DoingMaths
Chapter 4 8 Glencoe Precalculus Word Problem Practice Right Triangle Trigonometry 1 MONUMENTS The Leaning Tower of Pisa in Italy is about 55 9 meters tall and is leaning so it is only about 55 meters above the ground At what angle is the tower leaning? about 10 3° 2 SUBMARINES A submarine that is 250 meters below the surface of the ocean
C H A P T E R 4 Trigonometric Functions - Fraser HS Math
274 Chapter 4 Trigonometric Functions 12 (a) Coterminal angles for (b) Coterminal angles for 5p 4 2 2p5 2 3p 4 5p 4 1 2p5 13 p 4 5p 4: 7p 6 2 2p5 2 5p 6 7p 6 1 2p5 19 p 6 7p 6: 13 (a) Coterminal angles for
Trigonometry Worksheet T1 – Labelling Triangles
Trigonometry Worksheet T4 – Calculating Angles - ANSWERS 1 23 58o sin 0 4 sin 0 4 10 4 sin 1 = = = = ? s s s s 6 38 68o sin 0 625 sin 0 625 8 5 sin 1 = = = = ? b b b b 2 60o cos 0 5 cos 0 5 12 6 cos 1 = = = = ? c c c c 7 73 74o tan 3 428571429 tan 3 428571429 7 24 tan 1 = = = = ? z z z z 3 63 43o tan 2 tan 2 9 18 tan 1
What is a trigonometry worksheet?
A worksheet with various right-angles and isosceles triangles where trigonometry is needed to find the missing side lengths. This worksheet uses cos, sin and tan. A worksheet containing various right-angles triangles with missing angles, requiring the use of trigonometry to find them. This worksheet use sin, cos and tan.
What is Chapter 8 Introduction to trigonometry?
Class 10 Maths Chapter 8 Introduction to Trigonometry is included under Unit 5 Trigonometry of class 10 maths syllabus. Chapter 8 exercise 8.2 covers important questions based on trigonometric ratios of some specific angles. Download PDF: NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Exercise 8.2
What is trigonometry Unit 4?
The topics in this unit serve as the underpinning for trigonometry studied in Unit 4 and provide the first insight into geometry as a modeling tool for contextual situations. This unit begins with Topic A, Dilations off the Coordinate Plane. Students identify properties of dilations by performing dilations using constructions.
C H A P T E R 4
Trigonometric Functions
Section 4.1Radian and Degree Measure . . . . . . . . . . . . . . . .272 Section 4.2Trigonometric Functions: The Unit Circle . . . . . . . .281 Section 4.3Right Triangle Trigonometry . . . . . . . . . . . . . . . .289 Section 4.4Trigonometric Functions of Any Angle . . . . . . . . . .300 Section 4.5Graphs of Sine and Cosine Functions . . . . . . . . . . .317 Section 4.6Graphs of Other Trigonometric Functions . . . . . . . . .329 Section 4.7Inverse Trigonometric Functions . . . . . . . . . . . . . .339 Section 4.8Applications and Models . . . . . . . . . . . . . . . . . .350Review Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . .360
Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .377
© Houghton Mifflin Company. All rights reserved.C H A P T E R 4Trigonometric Functions
Section 4.1 Radian and Degree Measure
272You should know the following basic facts about angles, their measurement, and their applications.
?Types of Angles:(a) Acute: Measure between and (b) Right: Measure (c) Obtuse: Measure between and (d) Straight: Measure
?and are complementary if They are supplementary if ?Two angles in standard position that have the same terminal side are called coterminal angles. ?To convert degrees to radians, use radians. ?To convert radians to degrees, use 1 radian ?one minute of ?one second of ?The length of a circular arc is where is measured in radians. ?Speed ?Angular speed ???t?s?rt?distance?time ?s?r?1??1?60 of 1??1?36001??1??1?601
?180????.1? ? ??180 ????180?.????90?.??180?.180?.90?90?.90?.0?
1.The angle shown is approximately 2 radians.
Vocabulary Check
1.Trigonometry2.angle3.standard position4.coterminal
9.linear10.angular
2.The angle shown isapproximately radians.?4
3.(a) Since lies in Quadrant IV.(b) Since lies in
Quadrant II.
5? 2<11?4<3?, 11?
432<7?
4<2?, 7?
44.(a) Since lies in
Quadrant IV.
(b) Since lies inQuadrant II.?
3213?
9?, 13?
9? 25?12<0, 5?
2 © Houghton Mifflin Company. All rights reserved.Section 4.1 Radian and Degree Measure273
9.(a) (b) x y 322? 3 x 11 6π y11?
67.(a)(b)
x y 344? 3
43π
x y13?45.(a) Since lies in Quadrant IV.(b) Since lies in
Quadrant III.?
?2?2; ?2?
21<0; ?16.(a) Since 3.5 lies in Quadrant III.(b) Since 2.25 lies in Quadrant II.
2<2.25,
?<3.5<3? 2, 8.(a) (b) x y 52π-
?5? 2 x 74-π
y ?7? 410.(a) 4
(b) x y -3 ?3 x 4y11.(a) Coterminal angles for
6?2?? ?11?
66?2??13?
66:(b) Coterminal angles for
23?2?? ?4?
323?2??8?
323: © Houghton Mifflin Company. All rights reserved.
274Chapter 4 Trigonometric Functions
12.(a) Coterminal angles for
(b) Coterminal angles for 54?2?? ?3?
454?2??13?
454:7
6?2?? ?5?
676?2??19?
676:13.(a) Coterminal angles for
(b) Coterminal angles for 215?2?? ?32?
15? 215?2??28?
15? 2 15:? 94?4??7?
4? 94?2?? ??
4? 94:14.(a) Coterminal angles for
(b) Coterminal angles for 845?2?? ?82?
45845?2??98?
45845:7
8?2?? ?9?
878?2??23?
878:
15.Complement:Supplement:
3?2 3 2? 3? 617.Complement:Supplement:
6?5 6 2? 6?316.Complement: Not possible; is greater than
(a)Supplement:??3? 4? 4 2.3 418.Complement: Not possible; is greater than Supplement:
??2? 3? 3 2.2 319.Complement:Supplement:
??1?2.142?1?0.5720.Complement: None
Supplement:
??2?1.14?2>? 2? 21.The angle shown is approximately 210?.22.
The angle shown is approximately ?45?.
23.(a) Since lies in
Quadrant II.
(b) Since lies inQuadrant IV.282?270?
<282?<360?,150?90? <150?<180?,25.(a) Since
lies in Quadrant III. (b) Since lies in Quadrant I.?336? 30 ?360?336? 30?270?,?132? 50 ?180?132? 50?90?,24.(a) Since lies inQuadrant I.
(b) Since lies in Quadrant I.8.5?0? <8.5?<90?,87.9?0? <87.9?<90?,26.(a) Since
lies in Quadrant II. (b) Since lies in Quadrant IV.?12.35??90? 12.35? 0?,?245.25??270? 245.25?180?, © Houghton Mifflin Company. All rights reserved.Section 4.1 Radian and Degree Measure275
27.(a)
30?x y30?(b)
150°
x y150?28.(a)(b)
x -120° y ?120? x -270° y ?270?29.(a)(b)780°
x y 780?x
405°
y405?30.(a)(b)
x y -600? ?600? - °450 x y ?450?31.(a) Coterminal angles for (b) Coterminal angles for
?36? ?360? ? ?396??36? ?360? ?324??36?:52? ?360? ? ?308?52? ?360? ?412?52?:33.(a) Coterminal angles for
(b) Coterminal angles for230? ?360? ? ?130?230? ?360? ?590?230?:300? ?360? ? ?60?300? ?360? ?660?300?:32.(a) Coterminal angles for (b) Coterminal angles for
?390? ?360? ? ?30??390? ?720? ?330??390?:114? ?360? ? ?246?114? ?360? ?474?114?:34.(a) Coterminal angles for
(b) Coterminal angles for?740? ?720? ? ?20??740? ?1080? ?340??740?:?445? ?360? ? ?85??445? ?720? ?275??445?:35.Complement:Supplement: 180? ?24? ?156?90? ?24? ?66?36.Complement: Not possibleSupplement: 180? ?129? ?51?
37.Complement:Supplement: 180? ?87? ?93?90? ?87? ?3?38.Complement: Not possibleSupplement: 180? ?167? ?13?39.(a)(b) 150? ?150?
180???5?
630? ?30?
180????
6 © Houghton Mifflin Company. All rights reserved.276Chapter 4 Trigonometric Functions
44.(a)(b) 3
??3??180? ???540??4 ?? ?4??180? ??? ?720?46.(a)
(b) 2815?28
15?180?
???336?? 156? ?15
6?180?
??? ?450?45.(a)(b)?1360? ?13
60?180?
??? ?39?7 3?73?180?
???420?47.115? ?115
180???2.007 radians48.radians83.7? ?83.7???
180???1.461
50.radians?46.52? ? ?46.52?
180????0.81249.?216.35? ? ?216.35?
180????3.776 radians
51.?0.78? ? ?0.78
180????0.014 radians
53.7? 7? 180?
???25.714?55.6.5??6.5??180? ???1170?
61.85? 18
? 30??85? ??1860????30
3600???85.308?
63.?125? 36
?? ?125? ??363600??? ?125.01?
65.280.6? ?280? ?0.6
?60???280? 36?67.?345.12? ? ?345? 7? 12?
57.?2? ?2?
180?????114.592?
59.64? 45
??64? ??4560???64.75?52.radians395? ?395?
180???6.894
54.8 13?8
13?180?
???110.769?56.?4.2
?? ?4.2?? 180???? ?756?
58.?0.48? ?0.48
?180? ????27.502?60.?124? 30
?? ?124.5?62.?408? 16
? 25???408.274?64.330? 25
??330.007?66.?115.8? ? ?115? 48
?68.310.75? ?310? 45?43.(a)(b)?7
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