Unit T Student Success Sheet (SSS) Graphing Trig Functions (sections )
|
|
- Harvey Miller
- 5 years ago
- Views:
Transcription
1 Unit T Student Success Sheet (SSS) Graphing Trig Functions (sections ) Standards: Trig 4.0, 5.0,6.0 Segerstrom High School -- Math Analysis Honors Name: Period: Thinkbinder Study Group: Reminders: Practice Problems (PQ & PT) are completed in spiral bound notebook only. All pages in spiral notebook should be labeled accordingly: Unit Concept - (title of assignment) Examples: Unit T Concept 1 Practice Quiz Unit T Concept 1-4 Practice Test Website with all video links and resources: kirchmathanalysis.blogspot.com Edmodo Group Codes for class communication: Success means having the courage, the determination, and the will to become the person you believe you were meant to be George Sheehan Concept Mandatory # What we will be learning Practice Practice quiz 1 1 graphing sine and cosine 2 graphing secant and cosecant Practice quiz 2 3 graphing tangent and cotangent Practice quiz 3 Optional Extra practice from textbook This is our final chapter of trigonometry gosh how time flies! We will conclude our time by graphing the six main trigonometric functions. The blanks on page 2 are the most important things you need to know about trig graphs, so study those carefully! A few websites that will help in your understanding (also linked to on blog in MentorMob Playlist)
2 FINAL GRAPH MUST BE CLEARLY SEEN/LABELED/MARKED...I prefer that you do this in colored pencil so it stands out (NO PEN!). Do all work in pencil, and once you are sure of your final answer, go over it in color. Sine/Cosine I need to see 5 key points Cosecant/Secant I need to see original sine or cosine graph + asymptotes + 1 key point (mountain-top or valley-bottom) Tangent/Cotangent I need to see 1 key point + asymptotes THINGS TO KNOW ABOUT TRIGONOMETRIC GRAPHS 1. They are. This means they repeat themselves over and over again. One time through their cycle is called a. The end of one period is always the beginning of the next. When we draw our graphs, I only require you to draw out one period. However, you must know they go on forever and ever. 2. The period for sine, cosine, cosecant, and secant is. This means they go through one cycle while covering units on the x-axis 3. The period for tangent and cotangent is. This means they go through one cycle while covering units on the x-axis. 4. Cosecant and Secant have asymptotes where sine and cosine are equal to zero. This is because they are the of sine and cosine. Thus, if the value of sine is 0, the value of cosecant is 1/0, which is. Undefined = 5. Tangent and Cotangent have asymptotes where their respective ratios are equal to zero. Tangent = sine/cosine, so when cosine = 0, tangent has asymptotes. Tangent's parent asymptotes are thus at and (the two points on the unit circle where the x value is 0). Cotangent = cosine/sine, so when sine = 0, tangent has asymptotes. Cotangent's parent asymptotes are thus at and (the two points on the unit circle where the y value is 0). 6. Sine and cosine graphs have an. Amplitudes are the distance between the highest and lowest points on the graph. They can be found by looking at the equation at the value of. 7. Sine and cosine graphs look like 8. Cosecant and Secant graphs look like 9. Tangent and cotangent graphs look like
3 ---Unit T Student Success Sheet--- Graphing Trig Functions (sections )--- Math Analysis Honors--- [ ( )] WRITING EQUATIONS in graph-able form... First, You must factor out b first! Then, You must decide how to label your scale on your graph so it is easy for you to graph. 1. Find out period. The period for sin/csc and cos/sec is found by using. The period for tan/cot is found by using 2. Find out L/R shift (based on h ) 3. Pick scale that works easily with both period and shift. (usually based on the denominator of the shifted amount; sometimes if the period is also a fraction you have to find the LCD of the two)
4 PQ PROBLEMS: You must complete AT LEAST two graphs of each type (2 sine, 2 cosine, etc). It is suggested you complete all 8 problems for each concept. Print out the graphing chart to fill out for practice. Or, use graph paper and make your own template. Make sure to include all parts of the template if you hand-draw it. Video and Extra problems We will be working out several of these on video together. (#10,14,18,22,26,30) Any problems we don t complete on video can be completed for extra practice at home. Extra Problems # 7,8,11,12,15,16, 19,20,23,24,27,28 are already worked out for you to reference (no video, just work) Odds answer key Evens answer key
5 SAMPLE EQUATION f(x) = a. sin (b (x h) ) + k f(x) = a. cos (b (x h) ) + k amplitude period Plot parent points (5 total) a 2π b 1. plot beginning and end SINE GRAPHS **starts and ends at 0 1 mark = 1 mark = 2. plot middle 3. plot the midpoints of each segment **PLOT PARENT POINTS IN PENCIL **PLOT SHIFTED POINTS IN DIFFERENT COLOR COSINE GRAPHS **starts and ends at amplitude **DECIDE HOW YOU WILL LABEL YOUR SCALE BASED ON YOUR SHIFTS AND PERIOD right or left shift up or down shift Based on h Based on k DOMAIN X-values (interval notation) (-, ) - always (-, ) - always RANGE y-values (interval notation) Depends on amplitude and shifts [, ] Depends on amplitude and shifts [, ]
6 SAMPLE EQUATION **you will be sketching the corresponding sine and cosine graph first, so follow the same steps! amplitude a f(x) = a. csc (b (x h) ) + k f(x) = a. sec (b (x h) ) + k period Plot parent points (5 total) 2π b 1. plot beginning and end 1 mark = 1 mark = SINE GRAPHS **starts and ends at 0 will graph COSECANT 2. plot middle 3. plot the midpoints of each segment **PLOT PARENT POINTS IN PENCIL **PLOT SHIFTED POINTS IN DIFFERENT COLOR COSINE GRAPHS **starts and ends at amplitude will graph SECANT **DECIDE HOW YOU WILL LABEL YOUR SCALE BASED ON YOUR SHIFTS AND PERIOD right or left shift Based on h up or down shift Based on k k will always be 0 for us in this class k will always be 0 for us in this class INVERSE GRAPH You will have a sketch of the corresponding sine or cosine graph in light pencil, and then you will graph the reciprocal function in dark pencil based on the following requirements: 1. vertical asymptotes where the graph crosses the x-axis. X= + n (1 st one) + (½ the period)n 2. Draw graph (looks like a bunch of parabolas) on the mountains and valleys of the reciprocal graph 1. vertical asymptotes where the graph crosses the x-axis. X= + n (1 st one) + (½ the period)n 2. Draw graph (looks like a bunch of parabolas) on the mountains and valleys of the reciprocal graph DOMAIN X-values (interval notation) Depends on asymptotes. Write domain as x asymptotes Depends on asymptotes. Write domain as x asymptotes RANGE y-values (interval notation) Depends on amplitude and shifts (-, ] U [, ) Depends on amplitude and shifts (-, ] U [, )
7 f(x) = a. tan (b (x h) ) + k f(x) = a. cot (b (x h) ) + k SAMPLE EQUATION amplitude Tangent and cotangent graphs do not have amplitudes If a is positive, the graph will go uphill If a is positive, the graph will go downhill period right or left shift up or down shift π b Based on h *This shift is taken into account with your asymptotes (below) Based on k 1 mark = 1 mark = asymptotes b(x-h) = π/2 b(x-h) = -π/2 b(x-h) = 0 b(x-h) = π X= + n (1 st one) + (the period)n X= + n (1 st one) + (the period)n Plot parent points (5 total) 1. plot beginning and end asymptotes TANGENT GRAPHS 2. plot middle point, based on h and k (tangent starts at (0,0), while cotangent starts at ( π/2, 0) 3. Draw graph going uphill or downhill, as decided based on a **DECIDE HOW YOU WILL LABEL YOUR SCALE BASED ON YOUR SHIFTS AND PERIOD COTANGENT GRAPHS DOMAIN X-values (interval notation) Depends on asymptotes. Write domain as x asymptotes Depends on asymptotes. Write domain as x asymptotes RANGE y-values (interval notation) (-, ) - always (-, ) - always
8 Unit T Practice Test Worked out answer key and video answer key available See kirchmathanalysis.blogspot.com for answer keys and extra videos! Use the same directions from the PQ problems for each concept to solve these in order to prepare for the test. Answer key is posted online only at kirchmathanalysis.blogspot.com Worked out answer key available
Chapter 4. Trigonometric Functions. 4.6 Graphs of Other. Copyright 2014, 2010, 2007 Pearson Education, Inc.
Chapter 4 Trigonometric Functions 4.6 Graphs of Other Trigonometric Functions Copyright 2014, 2010, 2007 Pearson Education, Inc. 1 Objectives: Understand the graph of y = tan x. Graph variations of y =
More information4.6 GRAPHS OF OTHER TRIGONOMETRIC FUNCTIONS
4.6 GRAPHS OF OTHER TRIGONOMETRIC FUNCTIONS Copyright Cengage Learning. All rights reserved. What You Should Learn Sketch the graphs of tangent functions. Sketch the graphs of cotangent functions. Sketch
More informationMath 1330 Section 5.3 Graphs of the Tangent, Cotangent, Secant, and Cosecant Functions
Math 1330 Section 5.3 Graphs of the Tangent, Cotangent, Secant, and Cosecant Functions In this section, you will learn to graph the rest of the trigonometric functions. We can use some information from
More informationThis is called the horizontal displacement of also known as the phase shift.
sin (x) GRAPHS OF TRIGONOMETRIC FUNCTIONS Definitions A function f is said to be periodic if there is a positive number p such that f(x + p) = f(x) for all values of x. The smallest positive number p for
More informationModule 4 Graphs of the Circular Functions
MAC 1114 Module 4 Graphs of the Circular Functions Learning Objectives Upon completing this module, you should be able to: 1. Recognize periodic functions. 2. Determine the amplitude and period, when given
More informationUnit O Student Success Sheet (SSS) Right Triangle Trigonometry (sections 4.3, 4.8)
Unit O Student Success Sheet (SSS) Right Triangle Trigonometry (sections 4.3, 4.8) Standards: Geom 19.0, Geom 20.0, Trig 7.0, Trig 8.0, Trig 12.0 Segerstrom High School -- Math Analysis Honors Name: Period:
More informationGraphs of Other Trig Functions
Graph y = tan. y 0 0 6 3 3 3 5 6 3 3 1 Graphs of Other Trig Functions.58 3 1.7 undefined 3 3 3 1.7-1 0.58 3 CHAT Pre-Calculus 3 The Domain is all real numbers ecept multiples of. (We say the domain is
More informationSection 6.2 Graphs of the Other Trig Functions
Section 62 Graphs of the Other Trig Functions 369 Section 62 Graphs of the Other Trig Functions In this section, we will explore the graphs of the other four trigonometric functions We ll begin with the
More informationUnit R Student Success Sheet (SSS) Trigonometric Identities Part 2 (section 5.4)
Unit R Student Success Sheet (SSS) Trigonometric Identities Part 2 (section 5.4) Standards: Trig 10.0 Segerstrom High School -- Math Analysis Honors Name: Period: Thinkbinder Study Group: www.bit.ly/chatunitr
More informationBasic Graphs of the Sine and Cosine Functions
Chapter 4: Graphs of the Circular Functions 1 TRIG-Fall 2011-Jordan Trigonometry, 9 th edition, Lial/Hornsby/Schneider, Pearson, 2009 Section 4.1 Graphs of the Sine and Cosine Functions Basic Graphs of
More informationNotice there are vertical asymptotes whenever y = sin x = 0 (such as x = 0).
1 of 7 10/1/2004 6.4 GRAPHS OF THE OTHER CIRCULAR 6.4 GRAPHS OF THE OTHER CIRCULAR Graphs of the Cosecant and Secant Functions Graphs of the Tangent and Cotangent Functions Addition of Ordinates Graphs
More informationName: Teacher: Pd: Algebra 2/Trig: Trigonometric Graphs (SHORT VERSION)
Algebra 2/Trig: Trigonometric Graphs (SHORT VERSION) In this unit, we will Learn the properties of sine and cosine curves: amplitude, frequency, period, and midline. Determine what the parameters a, b,
More informationSection 5.3 Graphs of the Cosecant and Secant Functions 1
Section 5.3 Graphs of the Cosecant, Secant, Tangent, and Cotangent Functions The Cosecant Graph RECALL: 1 csc x so where sin x 0, csc x has an asymptote. sin x To graph y Acsc( Bx C) D, first graph THE
More informationChapter 5.6: The Other Trig Functions
Chapter 5.6: The Other Trig Functions The other four trig functions, tangent, cotangent, cosecant, and secant are not sinusoids, although they are still periodic functions. Each of the graphs of these
More informationMAT 115: Precalculus Mathematics Constructing Graphs of Trigonometric Functions Involving Transformations by Hand. Overview
MAT 115: Precalculus Mathematics Constructing Graphs of Trigonometric Functions Involving Transformations by Hand Overview Below are the guidelines for constructing a graph of a trigonometric function
More informationAP Calculus Summer Review Packet
AP Calculus Summer Review Packet Name: Date began: Completed: **A Formula Sheet has been stapled to the back for your convenience!** Email anytime with questions: danna.seigle@henry.k1.ga.us Complex Fractions
More informationWalt Whitman High School SUMMER REVIEW PACKET. For students entering AP CALCULUS BC
Walt Whitman High School SUMMER REVIEW PACKET For students entering AP CALCULUS BC Name: 1. This packet is to be handed in to your Calculus teacher on the first day of the school year.. All work must be
More informationJune 6 Math 1113 sec 002 Summer 2014
June 6 Math 1113 sec 002 Summer 2014 Sec. 6.4 Plotting f (x) = a sin(bx c) + d or f (x) = a cos(bx c) + d Amplitude is a. If a < 0 there is a reflection in the x-axis. The fundamental period is The phase
More informationMath 1330 Final Exam Review Covers all material covered in class this semester.
Math 1330 Final Exam Review Covers all material covered in class this semester. 1. Give an equation that could represent each graph. A. Recall: For other types of polynomials: End Behavior An even-degree
More informationPrecalculus: Graphs of Tangent, Cotangent, Secant, and Cosecant Practice Problems. Questions
Questions 1. Describe the graph of the function in terms of basic trigonometric functions. Locate the vertical asymptotes and sketch two periods of the function. y = 3 tan(x/2) 2. Solve the equation csc
More informationMath 144 Activity #3 Coterminal Angles and Reference Angles
144 p 1 Math 144 Activity #3 Coterminal Angles and Reference Angles For this activity we will be referring to the unit circle. Using the unit circle below, explain how you can find the sine of any given
More informationUnit 7: Trigonometry Part 1
100 Unit 7: Trigonometry Part 1 Right Triangle Trigonometry Hypotenuse a) Sine sin( α ) = d) Cosecant csc( α ) = α Adjacent Opposite b) Cosine cos( α ) = e) Secant sec( α ) = c) Tangent f) Cotangent tan(
More information4.1: Angles & Angle Measure
4.1: Angles & Angle Measure In Trigonometry, we use degrees to measure angles in triangles. However, degree is not user friendly in many situations (just as % is not user friendly unless we change it into
More information1. The circle below is referred to as a unit circle. Why is this the circle s name?
Right Triangles and Coordinates on the Unit Circle Learning Task: 1. The circle below is referred to as a unit circle. Why is this the circle s name? Part I 2. Using a protractor, measure a 30 o angle
More informationMastery. PRECALCULUS Student Learning Targets
PRECALCULUS Student Learning Targets Big Idea: Sequences and Series 1. I can describe a sequence as a function where the domain is the set of natural numbers. Connections (Pictures, Vocabulary, Definitions,
More informationLesson Goals. Unit 6 Introduction to Trigonometry Graphing Other Trig Functions (Unit 6.5) Overview. Overview
Unit 6 Introduction to Trigonometry Graphing Other Trig Functions (Unit 6.5) William (Bill) Finch Mathematics Department Denton High School Lesson Goals When you have completed this lesson you will: Graph
More information2.7 Graphing Tangent, Cotangent, Secant, and
www.ck12.org Chapter 2. Graphing Trigonometric Functions 2.7 Graphing Tangent, Cotangent, Secant, and Cosecant Learning Objectives Apply transformations to the remaining four trigonometric functions. Identify
More informationUnit R Student Success Sheet (SSS) Trigonometric Identities Part 2 (section 5.4)
Unit R Student Success Sheet (SSS) Trigonometric Identities Part 2 (section 5.4) Segerstrom High School Standards: Trig 10.0 Math Analysis Honors Name: Period: Mrs. Kirch: All Mornings 7-8am + after school
More informationUnit 6 Introduction to Trigonometry Graphing Other Trig Functions (Unit 6.5)
Unit 6 Introduction to Trigonometry Graphing Other Trig Functions (Unit 6.5) William (Bill) Finch Mathematics Department Denton High School Lesson Goals When you have completed this lesson you will: Graph
More information1. GRAPHS OF THE SINE AND COSINE FUNCTIONS
GRAPHS OF THE CIRCULAR FUNCTIONS 1. GRAPHS OF THE SINE AND COSINE FUNCTIONS PERIODIC FUNCTION A period function is a function f such that f ( x) f ( x np) for every real numer x in the domain of f every
More informationThe Sine and Cosine Functions
Concepts: Graphs of Tangent, Cotangent, Secant, and Cosecant. We obtain the graphs of the other trig functions by thinking about how they relate to the sin x and cos x. The Sine and Cosine Functions Page
More information8.6 Other Trigonometric Functions
8.6 Other Trigonometric Functions I have already discussed all the trigonometric functions and their relationship to the sine and cosine functions and the x and y coordinates on the unit circle, but let
More informationGraphs of the Circular Functions. Copyright 2017, 2013, 2009 Pearson Education, Inc.
4 Graphs of the Circular Functions Copyright 2017, 2013, 2009 Pearson Education, Inc. 1 4.3 Graphs of the Tangent and Cotangent Functions Graph of the Tangent Function Graph of the Cotangent Function Techniques
More informationMATH STUDENT BOOK. 12th Grade Unit 4
MATH STUDENT BOOK th Grade Unit Unit GRAPHING AND INVERSE FUNCTIONS MATH 0 GRAPHING AND INVERSE FUNCTIONS INTRODUCTION. GRAPHING 5 GRAPHING AND AMPLITUDE 5 PERIOD AND FREQUENCY VERTICAL AND HORIZONTAL
More informationVerifying Trigonometric Identities
40 Chapter Analytic Trigonometry. f x sec x Sketch the graph of y cos x Amplitude: Period: One cycle: first. The x-intercepts of y correspond to the vertical asymptotes of f x. cos x sec x 4 x, x 4 4,...
More informationMath 1330 Test 3 Review Sections , 5.1a, ; Know all formulas, properties, graphs, etc!
Math 1330 Test 3 Review Sections 4.1 4.3, 5.1a, 5. 5.4; Know all formulas, properties, graphs, etc! 1. Similar to a Free Response! Triangle ABC has right angle C, with AB = 9 and AC = 4. a. Draw and label
More informationLesson 10.1 TRIG RATIOS AND COMPLEMENTARY ANGLES PAGE 231
1 Lesson 10.1 TRIG RATIOS AND COMPLEMENTARY ANGLES PAGE 231 What is Trigonometry? 2 It is defined as the study of triangles and the relationships between their sides and the angles between these sides.
More information2.3 Circular Functions of Real Numbers
www.ck12.org Chapter 2. Graphing Trigonometric Functions 2.3 Circular Functions of Real Numbers Learning Objectives Graph the six trigonometric ratios as functions on the Cartesian plane. Identify the
More informationUsing Fundamental Identities. Fundamental Trigonometric Identities. Reciprocal Identities. sin u 1 csc u. sec u. sin u Quotient Identities
3330_050.qxd /5/05 9:5 AM Page 374 374 Chapter 5 Analytic Trigonometry 5. Using Fundamental Identities What you should learn Recognize and write the fundamental trigonometric identities. Use the fundamental
More informationA trigonometric ratio is a,
ALGEBRA II Chapter 13 Notes The word trigonometry is derived from the ancient Greek language and means measurement of triangles. Section 13.1 Right-Triangle Trigonometry Objectives: 1. Find the trigonometric
More informationDefinitions Associated w/ Angles Notation Visualization Angle Two rays with a common endpoint ABC
Preface to Chapter 5 The following are some definitions that I think will help in the acquisition of the material in the first few chapters that we will be studying. I will not go over these in class and
More informationChapter 4/5 Part 1- Trigonometry in Radians
Chapter 4/5 Part - Trigonometry in Radians Lesson Package MHF4U Chapter 4/5 Part Outline Unit Goal: By the end of this unit, you will be able to demonstrate an understanding of meaning and application
More informationto and go find the only place where the tangent of that
Study Guide for PART II of the Spring 14 MAT187 Final Exam. NO CALCULATORS are permitted on this part of the Final Exam. This part of the Final exam will consist of 5 multiple choice questions. You will
More informationUnit 3 Trig II. 3.1 Trig and Periodic Functions
Unit 3 Trig II AFM Mrs. Valentine Obj.: I will be able to use a unit circle to find values of sine, cosine, and tangent. I will be able to find the domain and range of sine and cosine. I will understand
More informationSNAP Centre Workshop. Introduction to Trigonometry
SNAP Centre Workshop Introduction to Trigonometry 62 Right Triangle Review A right triangle is any triangle that contains a 90 degree angle. There are six pieces of information we can know about a given
More informationTrigonometric Functions of Any Angle
Trigonometric Functions of Any Angle MATH 160, Precalculus J. Robert Buchanan Department of Mathematics Fall 2011 Objectives In this lesson we will learn to: evaluate trigonometric functions of any angle,
More informationPrecalculus Solutions Review for Test 6 LMCA Section
Precalculus Solutions Review for Test 6 LMCA Section 4.5-4.8 Memorize all of the formulas and identities. Here are some of the formulas for chapter 5. BasicTrig Functions opp y hyp r sin csc hyp r opp
More informationCW High School. Advanced Math A. 1.1 I can make connections between the algebraic equation or description for a function, its name, and its graph.
1. Functions and Math Models (10.00%) 1.1 I can make connections between the algebraic equation or description for a function, its name, and its graph. 4 Pro cient I can make connections between the algebraic
More informationx,,, (All real numbers except where there are
Section 5.3 Graphs of other Trigonometric Functions Tangent and Cotangent Functions sin( x) Tangent function: f( x) tan( x) ; cos( x) 3 5 Vertical asymptotes: when cos( x ) 0, that is x,,, Domain: 3 5
More informationTriangle Trigonometry
Honors Finite/Brief: Trigonometry review notes packet Triangle Trigonometry Right Triangles All triangles (including non-right triangles) Law of Sines: a b c sin A sin B sin C Law of Cosines: a b c bccos
More information8B.2: Graphs of Cosecant and Secant
Opp. Name: Date: Period: 8B.: Graphs of Cosecant and Secant Or final two trigonometric functions to graph are cosecant and secant. Remember that So, we predict that there is a close relationship between
More informationChapter 4 Using Fundamental Identities Section USING FUNDAMENTAL IDENTITIES. Fundamental Trigonometric Identities. Reciprocal Identities
Chapter 4 Using Fundamental Identities Section 4.1 4.1 USING FUNDAMENTAL IDENTITIES Fundamental Trigonometric Identities Reciprocal Identities csc x sec x cot x Quotient Identities tan x cot x Pythagorean
More informationPRECALCULUS MATH Trigonometry 9-12
1. Find angle measurements in degrees and radians based on the unit circle. 1. Students understand the notion of angle and how to measure it, both in degrees and radians. They can convert between degrees
More informationAlbertson AP Calculus AB AP CALCULUS AB SUMMER PACKET DUE DATE: The beginning of class on the last class day of the first week of school.
Albertson AP Calculus AB Name AP CALCULUS AB SUMMER PACKET 2017 DUE DATE: The beginning of class on the last class day of the first week of school. This assignment is to be done at you leisure during the
More informationTrigonometry. 9.1 Radian and Degree Measure
Trigonometry 9.1 Radian and Degree Measure Angle Measures I am aware of three ways to measure angles: degrees, radians, and gradians. In all cases, an angle in standard position has its vertex at the origin,
More informationUnit Circle. Project Response Sheet
NAME: PROJECT ACTIVITY: Trigonometry TOPIC Unit Circle GOALS MATERIALS Explore Degree and Radian Measure Explore x- and y- coordinates on the Unit Circle Investigate Odd and Even functions Investigate
More informationAlgebra II Trigonometric Functions
Slide 1 / 162 Slide 2 / 162 Algebra II Trigonometric Functions 2015-12-17 www.njctl.org Slide 3 / 162 Trig Functions click on the topic to go to that section Radians & Degrees & Co-terminal angles Arc
More informationTrigonometry To learn more about all our offerings Visit Knewton.com
Trigonometry 978-1-63545-099-6 To learn more about all our offerings Visit Knewton.com Source Author(s) (Text or Video) Title(s) Link (where applicable) OpenStax Jay Abramson, Arizona State University
More informationSection 5: Introduction to Trigonometry and Graphs
Section 5: Introduction to Trigonometry and Graphs The following maps the videos in this section to the Texas Essential Knowledge and Skills for Mathematics TAC 111.42(c). 5.01 Radians and Degree Measurements
More informationPre-calculus Chapter 4 Part 1 NAME: P.
Pre-calculus NAME: P. Date Day Lesson Assigned Due 2/12 Tuesday 4.3 Pg. 284: Vocab: 1-3. Ex: 1, 2, 7-13, 27-32, 43, 44, 47 a-c, 57, 58, 63-66 (degrees only), 69, 72, 74, 75, 78, 79, 81, 82, 86, 90, 94,
More informationMath 144 Activity #2 Right Triangle Trig and the Unit Circle
1 p 1 Right Triangle Trigonometry Math 1 Activity #2 Right Triangle Trig and the Unit Circle We use right triangles to study trigonometry. In right triangles, we have found many relationships between the
More informationGraphing Trigonometric Functions: Day 1
Graphing Trigonometric Functions: Day 1 Pre-Calculus 1. Graph the six parent trigonometric functions.. Apply scale changes to the six parent trigonometric functions. Complete the worksheet Exploration:
More informationPRESCOTT UNIFIED SCHOOL DISTRICT District Instructional Guide Revised 6/3/15
PRESCOTT UNIFIED SCHOOL DISTRICT District Instructional Guide Revised 6/3/15 Grade Level: PHS Subject: Precalculus Quarter/Semester: 1/1 Core Text: Precalculus with 1 st week Chapter P - Prerequisites
More informationSection 7.5 Inverse Trigonometric Functions II
Section 7.5 Inverse Trigonometric Functions II Note: A calculator is helpful on some exercises. Bring one to class for this lecture. OBJECTIVE 1: Evaluating composite Functions involving Inverse Trigonometric
More informationDear Accelerated Pre-Calculus Student:
Dear Accelerated Pre-Calculus Student: We are very excited that you have decided to take this course in the upcoming school year! This is a fast-paced, college-preparatory mathematics course that will
More informationFoundations of Math II
Foundations of Math II Unit 6b: Toolkit Functions Academics High School Mathematics 6.6 Warm Up: Review Graphing Linear, Exponential, and Quadratic Functions 2 6.6 Lesson Handout: Linear, Exponential,
More informationAlgebra II. Chapter 13 Notes Sections 13.1 & 13.2
Algebra II Chapter 13 Notes Sections 13.1 & 13.2 Name Algebra II 13.1 Right Triangle Trigonometry Day One Today I am using SOHCAHTOA and special right triangle to solve trig problems. I am successful
More informationTrigonometry and the Unit Circle. Chapter 4
Trigonometry and the Unit Circle Chapter 4 Topics Demonstrate an understanding of angles in standard position, expressed in degrees and radians. Develop and apply the equation of the unit circle. Solve
More informationAlgebra II. Slide 1 / 162. Slide 2 / 162. Slide 3 / 162. Trigonometric Functions. Trig Functions
Slide 1 / 162 Algebra II Slide 2 / 162 Trigonometric Functions 2015-12-17 www.njctl.org Trig Functions click on the topic to go to that section Slide 3 / 162 Radians & Degrees & Co-terminal angles Arc
More informationEssential Question What are the characteristics of the graph of the tangent function?
8.5 Graphing Other Trigonometric Functions Essential Question What are the characteristics of the graph of the tangent function? Graphing the Tangent Function Work with a partner. a. Complete the table
More informationDownloaded from
Top Concepts Class XI: Maths Ch : Trigonometric Function Chapter Notes. An angle is a measure of rotation of a given ray about its initial point. The original ray is called the initial side and the final
More informationReview of Trigonometry
Worksheet 8 Properties of Trigonometric Functions Section Review of Trigonometry This section reviews some of the material covered in Worksheets 8, and The reader should be familiar with the trig ratios,
More informationUnit 6 Introduction to Trigonometry Right Triangle Trigonomotry (Unit 6.1)
Unit 6 Introduction to Trigonometry Right Triangle Trigonomotry (Unit 6.1) William (Bill) Finch Mathematics Department Denton High School Lesson Goals When you have completed this lesson you will: Find
More informationVerify Trigonometric Identities
4.3 a., A..A; P..C TEKS Verify Trigonometric Identities Before You graphed trigonometric functions. Now You will verify trigonometric identities. Why? So you can model the path of Halley s comet, as in
More informationCCNY Math Review Chapters 5 and 6: Trigonometric functions and graphs
Ch 5. Trigonometry 6. Angles 6. Right triangles 6. Trig funs for general angles 5.: Trigonometric functions and graphs 5.5 Inverse functions CCNY Math Review Chapters 5 and 6: Trigonometric functions and
More informationChapter 5. An Introduction to Trigonometric Functions 1-1
Chapter 5 An Introduction to Trigonometric Functions Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1-1 5.1 A half line or all points extended from a single
More informationHiram High School Accelerated Pre-Calculus Summer Assignment
Hiram High School Accelerated Pre-Calculus Summer Assignment This is a fast-paced, college-preparatory course that will prepare you to be successful in college math and in AP Calculus. This is a rigorous
More informationUnit 4 Trigonometry. Study Notes 1 Right Triangle Trigonometry (Section 8.1)
Unit 4 Trigonometr Stud Notes 1 Right Triangle Trigonometr (Section 8.1) Objective: Evaluate trigonometric functions of acute angles. Use a calculator to evaluate trigonometric functions. Use trigonometric
More informationChapter 4: Trigonometry
Chapter 4: Trigonometry Section 4-1: Radian and Degree Measure INTRODUCTION An angle is determined by rotating a ray about its endpoint. The starting position of the ray is the of the angle, and the position
More information( ) = 1 4. (Section 4.6: Graphs of Other Trig Functions) Example. Use the Frame Method to graph one cycle of the graph of
(Section 4.6: Graphs of Other Trig Functions) 4.63 Example Use the Frame Method to graph one cycle of the graph of y = 2 tan 2 5 x 3. (There are infinitely many possible cycles.) Solution Fortunately,
More informationTrigonometric ratios provide relationships between the sides and angles of a right angle triangle. The three most commonly used ratios are:
TRIGONOMETRY TRIGONOMETRIC RATIOS If one of the angles of a triangle is 90º (a right angle), the triangle is called a right angled triangle. We indicate the 90º (right) angle by placing a box in its corner.)
More informationSECTION 6-8 Graphing More General Tangent, Cotangent, Secant, and Cosecant Functions
6-8 Graphing More General Tangent, Cotangent, Secant, and Cosecant Functions 9 duce a scatter plot in the viewing window. Choose 8 for the viewing window. (B) It appears that a sine curve of the form k
More informationProof of Identities TEACHER NOTES MATH NSPIRED. Math Objectives. Vocabulary. About the Lesson. TI-Nspire Navigator System
Math Objectives Students will be able to interpret reciprocal, negative angle, cofunction, and Pythagorean identities in terms of the graphs of the trigonometric functions involved Students will be able
More informationA lg e b ra II. Trig o n o m e tric F u n c tio
1 A lg e b ra II Trig o n o m e tric F u n c tio 2015-12-17 www.njctl.org 2 Trig Functions click on the topic to go to that section Radians & Degrees & Co-terminal angles Arc Length & Area of a Sector
More informationA Quick Review of Trigonometry
A Quick Review of Trigonometry As a starting point, we consider a ray with vertex located at the origin whose head is pointing in the direction of the positive real numbers. By rotating the given ray (initial
More information45 Wyner Math Academy I Spring 2016
45 Wyner Math cademy I Spring 2016 HPTER FIVE: TRINGLES Review January 13 Test January 21 Other than circles, triangles are the most fundamental shape. Many aspects of advanced abstract mathematics and
More informationImportant. Compact Trigonometry CSO Prioritized Curriculum. Essential. Page 1 of 6
Essential Important Compact Trigonometry CSO Prioritized Curriculum M.O.T.3.1 apply the right triangle definition of the six trigonometric functions of an angle to determine the values of the function
More informationPRECALCULUS MR. MILLER
PRECALCULUS MR. MILLER I. COURSE DESCRIPTION This course requires students to use symbolic reasoning and analytical methods to represent mathematical situations, to express generalizations, and to study
More informationMath-3 Lesson 6-1. Trigonometric Ratios for Right Triangles and Extending to Obtuse angles.
Math-3 Lesson 6-1 Trigonometric Ratios for Right Triangles and Extending to Obtuse angles. Right Triangle: has one angle whose measure is. 90 The short sides of the triangle are called legs. The side osite
More informationMath12 Pre-Calc Review - Trig
Math1 Pre-Calc Review - Trig Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which of the following angles, in degrees, is coterminal with, but not equal
More informationInstructor s Commentary
Instructor s Commentary The following pages present information useful to instructors for planning the presentation of the materials in the text. Commentary for each section includes The objective of the
More informationCommon Core Standards Addressed in this Resource
Common Core Standards Addressed in this Resource N-CN.4 - Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular
More informationAP Calculus AB Summer Review Packet
AP Calculus AB Summer Review Packet Mr. Burrows Mrs. Deatherage 1. This packet is to be handed in to your Calculus teacher on the first day of the school year. 2. All work must be shown on separate paper
More informationVertical and Horizontal Translations
SECTION 4.3 Vertical and Horizontal Translations Copyright Cengage Learning. All rights reserved. Learning Objectives 1 2 3 4 Find the vertical translation of a sine or cosine function. Find the horizontal
More informationPART I: NO CALCULATOR (64 points)
Math 10 Trigonometry 11 th edition Lial, Hornsby, Schneider, and Daniels Practice Midterm (Ch. 1-) PART I: NO CALCULATOR (6 points) (.1,.,.,.) Match each graph with one of the basic circular functions
More informationSum and Difference Identities. Cosine Sum and Difference Identities: cos A B. does NOT equal cos A. Cosine of a Sum or Difference. cos B.
7.3 Sum and Difference Identities 7-1 Cosine Sum and Difference Identities: cos A B Cosine of a Sum or Difference cos cos does NOT equal cos A cos B. AB AB EXAMPLE 1 Finding Eact Cosine Function Values
More informationName Student Activity
Open the TI-Nspire document Proofs_of_Identities.tns. An identity is an equation that is true for all values of the variables for which both sides of the equation are defined. In this activity, you will
More informationHonors Precalculus: Solving equations and inequalities graphically and algebraically. Page 1
Solving equations and inequalities graphically and algebraically 1. Plot points on the Cartesian coordinate plane. P.1 2. Represent data graphically using scatter plots, bar graphs, & line graphs. P.1
More informationCatholic Central High School
Catholic Central High School Algebra II Practice Examination I Instructions: 1. Show all work on the test copy itself for every problem where work is required. Points may be deducted if insufficient or
More informationUnit 13: Periodic Functions and Trig
Date Period Unit 13: Periodic Functions and Trig Day Topic 0 Special Right Triangles and Periodic Function 1 Special Right Triangles Standard Position Coterminal Angles 2 Unit Circle Cosine & Sine (x,
More information