Math 2412 Activity 4(Due with Final Exam)
|
|
- Justin Logan
- 5 years ago
- Views:
Transcription
1 Math Activity (Due with Final Exam) Use properties of similar triangles to find the values of x and y x y 7 7 x 5 x y 7 For the angle in standard position with the point 5, on its terminal side, find the values of the six trigonometric functions: 5, sin cos tan csc sec cot
2 3 Find one solution of the equation sin 0 cos3 0 {Hint: cos x sin90 x } Find all the trigonometric function values of, if csc and is in Quadrant III sin cos tan csc sec cot 5 Find the exact value of each labeled part: a q m n q 5 n 60 m a 7 6 Find all the exact trigonometric function values of 590 sin590 cos590 tan590 csc590
3 sec590 cot590 7 Solve the right triangle to the nearest tenth of a degree and tenth of a foot: A b 895 ft C a 79 B m A b a 8 Solve the right triangle to the nearest degree and the nearest foot: A 37 ft c C 56 ft B
4 9 Find h to the nearest tenth h 35 {Hint: cot 35 x x h and cot 35 x35 x 35 } h h h 0 Find h to the nearest tenth x h {Hint: cot 35 x and cot 35 x h x h } Find the area of the indicated sector: 5 8
5 Find the measure of the central angle,, in radians The rotation of the larger wheel causes the smaller wheel to rotate Find the radius of the larger wheel if the smaller wheel rotates 90 when the larger wheel rotates 60 ft r Graph the function y cos x on the interval 0,
6 5 Graph the function y 3 sin x on the interval 3 0, Graph the function y3sin x 3 on the interval 0, 3 5
7 7 Graph the function y3cosx on the interval, 8 8
8 sin Graph the function y x on the interval,
9 7 9 Graph the function y3secx on the interval, Graph the function y csc x on the interval 3, 3
10 sec Graph the function y x on the interval, x Graph the function y tan on the interval 5, 3 5 3
11 3 Graph the function y 3cot x on the interval, Graph the function y tan x on the interval 3 3,6
12 5 Determine the range of the following functions: a) y 3sin x 7 b) y x sec 8 6 Verify the identity 7 Verify the identity cos x sin x cos x tan x sec x sec x cos sin sec cos x x x x 8 Show that the equation cosx cos x sin x is not an identity by demonstrating that for a specific value of x it is false 9 Show that the equation sinx sin x cos x is not an identity by demonstrating that for a specific value of x it is false 30 Find the exact value of cos65 3 Find an exact value of that makes cot 0 tan 0 3 Verify the identity cos 90 sin sin cos true x x x x 33 Find the exact value of cos cos9 sin sin9 3 Find the exact value of tan tan tan tan Find the exact value of sin65 36 Verify the identity tan x y tan y x tan x tan y tan xtan y 37 Verify the identity sin x y cot x cot y cos x y cot xcot y 38 Find the exact value of cos sin 39 Find the exact value of sin5 cos5 0 Verify the identity cos x cot x sin x
13 tan Verify the identity tan x x cosx Find the exact value of cot, if x 3 Verify the identity tan csc x cot x 5 tan and Verify the identity tan cos x tan x x 5 Find the exact value of 6 Find the exact value of 7 Find the exact value of 8 Find the exact value of sin sec 3 tan cos cos sin 3 5 cos Find the exact value of 50 Solve the equation 5 Solve the equation sin sin 3 cos cos 0 on the interval sin 0 on the interval 0, 0, 5 Solve the equation 53 Solve the equation sec tan on the interval cos sin 0, on the interval 0, 5 Solve the equation cos x 0 on the interval 0, 55 Solve the equation cos x sin x 0 on the interval 0, x 56 Solve the equation tan sin x on the interval 0,
14 57 Solve the equation sin cos x x on the interval 0, Sketch the solutions of the following polar coordinate equations 58 r sin 59 r cos 60 r cos 6 r cos 6 r cos Find the points of intersection of the solution curves of the following pairs of polar coordinate equations 63 r cos, r cos 6 rcos3, r
15 Find the points of intersection of the curves defined by the following parametric equations 65 xt yt ; 3 t and xs ; 3 s ys 66 x cost ;0 t y 3sint x sec s and ; 3 s 3 y tan s
16 67 x cost y sin t ;0 t and x cos s ;0 s y sin s 68 Find the exact value of each part labeled with a variable 8 y w x z 69 The tires of a bicycle have a radius of 5 ft, and are turning at the rate of 5 revolutions per second How fast is the bicycle traveling in feet per second?
17 70 If tan x 75 and cos 8 7 Find the exact value of cos x, then find the value of tan x cos x {Hint: 3 and cos A B cos Acos B cos Acos B } 7 Find the exact value of 5 tan {Hint: 5 6 and tan A B tan A tan B } tan Atan B 73 Find the exact value of cos A cos A {Hint: cos and 6 } Find the exact value of the following: 7 sinsin 75 sin sin 3 76 cossin 3 77 sin tan 78 tancos For each of the following, find sin x y, cos x y, tan x y, and the quadrant of x y sin x, cos y, x in quadrant I, y in quadrant IV 0 5 sin y, cos x, x in quadrant II, y in quadrant III 3 5
18 Find the sine and cosine of the following 8 B, given cosb, B in quadrant IV 8 y, given 8 5 sec y, sin y 0 3 Find the following: A 83 sin, given 3 cos A, with 90 A 80 b) sin x, given sin x 6, with x 8 sin y, given cosy, with y 3 Exactly solve the following trigonometric equations on the interval 0, 85 sin x 86 3cos x cos x 0 87 x x sec x 88 csc sin sin x sinx 90 cosxcos x 0 9 sin x cos x 9 sin3x 0 93 cos x 9 6 sin x cos x 95 6sin x7sin x 0 96 Sketch the graph of the solution to the polar coordinate equation r sin r
19 97 Sketch the graph of the solution to the polar coordinate equation r cos r 3 98 Find the points of intersection of the solution curves of the polar coordinate equations r cos and r sin 99 Find the points of intersection of the solution curves of the polar coordinate equations r sin and r sin cos
20 00 Graph the function y tan x on the interval, 0 Graph the function y sinx on the interval 0, 0 Determine the range of the function y x 03 If 3 8sin 5 7 cos x, then find the exact value of sin xtan x sin xcot x Find the exact value of the following 0 sincos sin sin tan sin 3 sin 3 {Hint: {Hint: sin A sin Acos A} sin A B sin Acos B cos Asin B } {Hint: tan A sin A cos A } cos A sin A 07 cos sin 08 Sketch the graph of the solution to the polar coordinate equation r cos r
21 09 Sketch the graph of the solution to the polar coordinate equation r sin r Find the points of intersection of the solution curves of the polar coordinate equations r sin and r 3sin
22 Find the points of intersection of the solution curves of the polar coordinate equations r sin and r Find the area of the region that is inside the solution curve of r sin but outside the solution curve of r sin 3 Given that a i 3j and b i j and another vector r 6i 7j, find numbers k and m so that r ka mb Express c in terms of a and b, given that the tip of c bisects the line segment b a c 5 For what values of x are xi j and xi xj orthogonal?
23 6 Given that a i xj and b i yj, find all values of x and y so that a b and a b 7 Use the dot-product to show that an angle inscribed in a semi-circle is a right angle (Look at a b a b ) a b a a b b b 8 Show that the sum of the squares of the lengths of the diagonals of a parallelogram equals the sum of the squares of the lengths of the four sides a Expand a b a b by using the dot-product b a b b a b a 9 It looks as if a b and a b are orthogonal Is this mere coincidence, or are there circumstances where we would expect the sum and difference of two vectors to be orthogonal? Find out by expanding a b a b 0 a b b a b a b
24 0 Given vectors a and b, let m a and n b, show that a) na mb and na mb are orthogonal b) c na mb bisects the angle between a and b Find all vectors v in the plane so that v and vi Graph each parabola x y 3 y x x 8x 8y Graph each ellipse 5 x y x 6y x 5y x 8x y 8y 3 0 Graph each hyperbola 9 x y y x 3 x 5y x 8x y 8y Find an equation for the parabola with focus of, and directrix of y
25 3 Find an equation of the hyperbola satisfying the given conditions: Endpoints of transverse axis:,0,,0 ; asymptote y x 35 Solve the system x x y 9 y 9 Solve the following systems of equations Check to see if your answer agrees with the graph x y (line) 36 y x (parabola) 37 x y 5 (circle) 3x y 5 (line)
26 x y (hyperbola) 38 x y (ellipse) x y (ellipse) 3 5 x y (hyperbola) 0 y x x (parabola) y x (parabola) y x (parabola) x y 6 (ellipse)
27 Find the values of x and y in the figure x 0 7 y 9 3 Express the product of the following complex numbers in standard form a) z 3cos00 i sin00, w cos60 i sin 60 b) z cos0 isin0, w 6cos5 isin5 Express the following in standard form a) 3 3 cos80 isin80 b) 5 cos isin On a recent episode of Who Wants to Be a Millionaire with Cedric the Entertainer, the following question appeared For which of the following times will the minute and hour hands of a clock form a right angle? a) :05 b) 5:0 c) 3:35 d) :50 The contestant chose answer a) and he was told that he was correct He wasn t correct, in fact, none of the options are correct Let s use basic trigonometry to find all the times for which the minute and hour hands form a right angle For t measured in minutes after M t t H t t midnight, 30 represents the cumulative angle of the minute hand, and 360 represents the cumulative angle of the hour hand In order for the two hands to form a right angle, the difference between the cumulative angle of the minute hand and the cumulative angle of the hour hand must be an odd multiple of So we get that
28 t n n n M t H t n ; n,, t t n ; n,, ;,, 80 t ; n,, a) Use the previous formula to find the number of times from one midnight to the next that the minute and hour hands form a right angle {Hint: 80 n # of minutes in a hour period } b) Use the same reasoning to find a formula for the times(in minutes after midnight) from one midnight to the next(inclusive) that the minute and hour hands point in exactly the same direction, and the number of times that it occurs c) Use the same reasoning to find a formula for the times(in minutes after midnight) from one midnight to the next that the minute and hour hands point in exactly opposite directions, and the number of times that it occurs
29 6 a) Use geometry to fill in all the missing angles and sides in the following diagram of right triangle ABC inscribed inside rectangle ADEF A 5 30 F C 90 D 60 B 90 E b) Use the diagram to find the exact values of the sine, cosine, tangent, cotangent, secant, and cosecant of the angles 5 and 75
Math 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 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 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 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 informationChapter 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 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 informationMidterm Review January 2018 Honors Precalculus/Trigonometry
Midterm Review January 2018 Honors Precalculus/Trigonometry Use the triangle below to find the exact value of each of the trigonometric functions in questions 1 6. Make sure your answers are completely
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 informationTo sketch the graph we need to evaluate the parameter t within the given interval to create our x and y values.
Module 10 lesson 6 Parametric Equations. When modeling the path of an object, it is useful to use equations called Parametric equations. Instead of using one equation with two variables, we will use two
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 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 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 informationPre Calculus Worksheet: Fundamental Identities Day 1
Pre Calculus Worksheet: Fundamental Identities Day 1 Use the indicated strategy from your notes to simplify each expression. Each section may use the indicated strategy AND those strategies before. Strategy
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 informationUse the indicated strategy from your notes to simplify each expression. Each section may use the indicated strategy AND those strategies before.
Pre Calculus Worksheet: Fundamental Identities Day 1 Use the indicated strategy from your notes to simplify each expression. Each section may use the indicated strategy AND those strategies before. Strategy
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 2 Intro to Angles and Trigonometry
HARTFIELD PRECALCULUS UNIT 2 NOTES PAGE 1 Unit 2 Intro to Angles and Trigonometry This is a BASIC CALCULATORS ONLY unit. (2) Definition of an Angle (3) Angle Measurements & Notation (4) Conversions of
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 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 informationPart I. There are 5 problems in Part I, each worth 5 points. No partial credit will be given, so be careful. Circle the correct answer.
Math 109 Final Exam-Spring 016 Page 1 Part I. There are 5 problems in Part I, each worth 5 points. No partial credit will be given, so be careful. Circle the correct answer. 1) Determine an equivalent
More informationMA 154 PRACTICE QUESTIONS FOR THE FINAL 11/ The angles with measures listed are all coterminal except: 5π B. A. 4
. If θ is in the second quadrant and sinθ =.6, find cosθ..7.... The angles with measures listed are all coterminal except: E. 6. The radian measure of an angle of is: 7. Use a calculator to find the sec
More informationUnit 3 Trigonometry. 3.4 Graph and analyze the trigonometric functions sine, cosine, and tangent to solve problems.
1 General Outcome: Develop trigonometric reasoning. Specific Outcomes: Unit 3 Trigonometry 3.1 Demonstrate an understanding of angles in standard position, expressed in degrees and radians. 3. Develop
More informationSection 7.1. Standard position- the vertex of the ray is at the origin and the initial side lies along the positive x-axis.
1 Section 7.1 I. Definitions Angle Formed by rotating a ray about its endpoint. Initial side Starting point of the ray. Terminal side- Position of the ray after rotation. Vertex of the angle- endpoint
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 informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Precalculus CP Final Exam Review - 01 Name Date: / / MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Convert the angle in degrees to radians. Express
More informationPART I You must complete this portion of the test without using a calculator. After you
Salt Lake Community College Math 1060 Final Exam A Fall Semester 2010 Name: Instructor: This Exam has three parts. Please read carefully the directions for each part. All problems are of equal point value.
More informationTrigonometry I. Exam 0
Trigonometry I Trigonometry Copyright I Standards 006, Test Barry Practice Mabillard. Exam 0 www.math0s.com 1. The minimum and the maximum of a trigonometric function are shown in the diagram. a) Write
More informationPLANE TRIGONOMETRY Exam I September 13, 2007
Name Rec. Instr. Rec. Time PLANE TRIGONOMETRY Exam I September 13, 2007 Page 1 Page 2 Page 3 Page 4 TOTAL (10 pts.) (30 pts.) (30 pts.) (30 pts.) (100 pts.) Below you will find 10 problems, each worth
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 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 informationName Trigonometric Functions 4.2H
TE-31 Name Trigonometric Functions 4.H Ready, Set, Go! Ready Topic: Even and odd functions The graphs of even and odd functions make it easy to identify the type of function. Even functions have a line
More informationMATH 1112 Trigonometry Final Exam Review
MATH 1112 Trigonometry Final Exam Review 1. Convert 105 to exact radian measure. 2. Convert 2 to radian measure to the nearest hundredth of a radian. 3. Find the length of the arc that subtends an central
More information1) The domain of y = sin-1x is The range of y = sin-1x is. 2) The domain of y = cos-1x is The range of y = cos-1x is
MAT 204 NAME TEST 4 REVIEW ASSIGNMENT Sections 8.1, 8.3-8.5, 9.2-9.3, 10.1 For # 1-3, fill in the blank with the appropriate interval. 1) The domain of y = sin-1x is The range of y = sin-1x is 2) The domain
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 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 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 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 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 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 informationYou ll use the six trigonometric functions of an angle to do this. In some cases, you will be able to use properties of the = 46
Math 1330 Section 6.2 Section 7.1: Right-Triangle Applications In this section, we ll solve right triangles. In some problems you will be asked to find one or two specific pieces of information, but often
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 informationToday we will focus on solving for the sides and angles of non-right triangles when given two angles and a side.
5.5 The Law of Sines Pre-Calculus. Use the Law of Sines to solve non-right triangles. Today we will focus on solving for the sides and angles of non-right triangles when given two angles and a side. Derivation:
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 informationMATH 122 Final Exam Review Precalculus Mathematics for Calculus, 7 th ed., Stewart, et al. by hand.
MATH 1 Final Exam Review Precalculus Mathematics for Calculus, 7 th ed., Stewart, et al 5.1 1. Mark the point determined by 6 on the unit circle. 5.3. Sketch a graph of y sin( x) by hand. 5.3 3. Find the
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 information5.2 Verifying Trigonometric Identities
360 Chapter 5 Analytic Trigonometry 5. Verifying Trigonometric Identities Introduction In this section, you will study techniques for verifying trigonometric identities. In the next section, you will study
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 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 informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Convert the angle to decimal degrees and round to the nearest hundredth of a degree. 1)
More informationsin30 = sin60 = cos30 = cos60 = tan30 = tan60 =
Precalculus Notes Trig-Day 1 x Right Triangle 5 How do we find the hypotenuse? 1 sinθ = cosθ = tanθ = Reciprocals: Hint: Every function pair has a co in it. sinθ = cscθ = sinθ = cscθ = cosθ = secθ = cosθ
More information5.1 Angles & Their Measures. Measurement of angle is amount of rotation from initial side to terminal side. radians = 60 degrees
.1 Angles & Their Measures An angle is determined by rotating array at its endpoint. Starting side is initial ending side is terminal Endpoint of ray is the vertex of angle. Origin = vertex Standard Position:
More informationPlane Trigonometry Test File Fall 2014
Plane Trigonometry Test File Fall 2014 Test #1 1.) Fill in the blanks in the two tables with the EXACT values (no calculator) of the given trigonometric functions. The total point value for the tables
More informationCh 7 & 8 Exam Review. Note: This is only a sample. Anything covered in class or homework may appear on the exam.
Ch 7 & 8 Exam Review Note: This is only a sample. Anything covered in class or homework may appear on the exam. Determine whether there is sufficient information for solving a triangle, with the given
More informationFind the amplitude, period, and phase shift, and vertical translation of the following: 5. ( ) 6. ( )
1. Fill in the blanks in the following table using exact values. Reference Angle sin cos tan 11 6 225 2. Find the exact values of x that satisfy the given condition. a) cos x 1, 0 x 6 b) cos x 0, x 2 3.
More informationTrigonometry. Secondary Mathematics 3 Page 180 Jordan School District
Trigonometry Secondary Mathematics Page 80 Jordan School District Unit Cluster (GSRT9): Area of a Triangle Cluster : Apply trigonometry to general triangles Derive the formula for the area of a triangle
More informationSecondary Mathematics 3 Table of Contents
Secondary Mathematics Table of Contents Trigonometry Unit Cluster 1: Apply trigonometry to general triangles (G.SRT.9)...4 (G.SRT.10 and G.SRT.11)...7 Unit Cluster : Extending the domain of trigonometric
More informationMAC Learning Objectives. Learning Objectives (Cont.) Module 2 Acute Angles and Right Triangles
MAC 1114 Module 2 Acute Angles and Right Triangles Learning Objectives Upon completing this module, you should be able to: 1. Express the trigonometric ratios in terms of the sides of the triangle given
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 informationSHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Review for Test 2 MATH 116 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the right triangle. If two sides are given, give angles in degrees and
More informationf sin the slope of the tangent line is given by f sin f cos cos sin , but it s also given by 2. So solve the DE with initial condition: sin cos
Math 414 Activity 1 (Due by end of class August 1) 1 Four bugs are placed at the four corners of a square with side length a The bugs crawl counterclockwise at the same speed and each bug crawls directly
More informationWhen you dial a phone number on your iphone, how does the
5 Trigonometric Identities When you dial a phone number on your iphone, how does the smart phone know which key you have pressed? Dual Tone Multi-Frequency (DTMF), also known as touch-tone dialing, was
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 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 informationAdvanced Math Final Exam Review Name: Bornoty May June Use the following schedule to complete the final exam review.
Advanced Math Final Exam Review Name: Bornoty May June 2013 Use the following schedule to complete the final exam review. Homework will e checked in every day. Late work will NOT e accepted. Homework answers
More informationMATH EXAM 1 - SPRING 2018 SOLUTION
MATH 140 - EXAM 1 - SPRING 018 SOLUTION 8 February 018 Instructor: Tom Cuchta Instructions: Show all work, clearly and in order, if you want to get full credit. If you claim something is true you must
More informationMid-Chapter Quiz: Lessons 9-1 through 9-3
Graph each point on a polar grid. 1. A( 2, 45 ) 3. Because = 45, locate the terminal side of a 45 angle with the polar axis as its initial side. Because r = 2, plot a point 2 units from the pole in the
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 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 informationMATHEMATICS 105 Plane Trigonometry
Chapter I THE TRIGONOMETRIC FUNCTIONS MATHEMATICS 105 Plane Trigonometry INTRODUCTION The word trigonometry literally means triangle measurement. It is concerned with the measurement of the parts, sides,
More informationMATH 1113 Exam 3 Review. Fall 2017
MATH 1113 Exam 3 Review Fall 2017 Topics Covered Section 4.1: Angles and Their Measure Section 4.2: Trigonometric Functions Defined on the Unit Circle Section 4.3: Right Triangle Geometry Section 4.4:
More information9.1 Use Trigonometry with Right Triangles
9.1 Use Trigonometry with Right Triangles Use the Pythagorean Theorem to find missing lengths in right triangles. Find trigonometric ratios using right triangles. Use trigonometric ratios to find angle
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 informationRewrite the equation in the left column into the format in the middle column. The answers are in the third column. 1. y 4y 4x 4 0 y k 4p x h y 2 4 x 0
Pre-Calculus Section 1.1 Completing the Square Rewrite the equation in the left column into the format in the middle column. The answers are in the third column. 1. y 4y 4x 4 0 y k 4p x h y 4 x 0. 3x 3y
More information5.5 Multiple-Angle and Product-to-Sum Formulas
Section 5.5 Multiple-Angle and Product-to-Sum Formulas 87 5.5 Multiple-Angle and Product-to-Sum Formulas Multiple-Angle Formulas In this section, you will study four additional categories of trigonometric
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 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 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 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 informationLesson 26 - Review of Right Triangle Trigonometry
Lesson 26 - Review of Right Triangle Trigonometry PreCalculus Santowski PreCalculus - Santowski 1 (A) Review of Right Triangle Trig Trigonometry is the study and solution of Triangles. Solving a triangle
More information: Find the values of the six trigonometric functions for θ. Special Right Triangles:
ALGEBRA 2 CHAPTER 13 NOTES Section 13-1 Right Triangle Trig Understand and use trigonometric relationships of acute angles in triangles. 12.F.TF.3 CC.9- Determine side lengths of right triangles by using
More informationIn a right triangle, the sum of the squares of the equals the square of the
Math 098 Chapter 1 Section 1.1 Basic Concepts about Triangles 1) Conventions in notation for triangles - Vertices with uppercase - Opposite sides with corresponding lower case 2) Pythagorean theorem In
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 informationPolar (BC Only) They are necessary to find the derivative of a polar curve in x- and y-coordinates. The derivative
Polar (BC Only) Polar coordinates are another way of expressing points in a plane. Instead of being centered at an origin and moving horizontally or vertically, polar coordinates are centered at the pole
More informationPerimeter. Area. Surface Area. Volume. Circle (circumference) C = 2πr. Square. Rectangle. Triangle. Rectangle/Parallelogram A = bh
Perimeter Circle (circumference) C = 2πr Square P = 4s Rectangle P = 2b + 2h Area Circle A = πr Triangle A = bh Rectangle/Parallelogram A = bh Rhombus/Kite A = d d Trapezoid A = b + b h A area a apothem
More informationYoungstown State University Trigonometry Final Exam Review (Math 1511)
Youngstown State University Trigonometry Final Exam Review (Math 1511) 1. Convert each angle measure to decimal degree form. (Round your answers to thousandths place). a) 75 54 30" b) 145 18". Convert
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 informationMATH 1020 WORKSHEET 10.1 Parametric Equations
MATH WORKSHEET. Parametric Equations If f and g are continuous functions on an interval I, then the equations x ft) and y gt) are called parametric equations. The parametric equations along with the graph
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 informationMultivariable Calculus
Multivariable Calculus Chapter 10 Topics in Analytic Geometry (Optional) 1. Inclination of a line p. 5. Circles p. 4 9. Determining Conic Type p. 13. Angle between lines p. 6. Parabolas p. 5 10. Rotation
More informationCLEP Pre-Calculus. Section 1: Time 30 Minutes 50 Questions. 1. According to the tables for f(x) and g(x) below, what is the value of [f + g]( 1)?
CLEP Pre-Calculus Section : Time 0 Minutes 50 Questions For each question below, choose the best answer from the choices given. An online graphing calculator (non-cas) is allowed to be used for this section..
More informationLook up partial Decomposition to use for problems #65-67 Do Not solve problems #78,79
Franklin Township Summer Assignment 2017 AP calculus AB Summer assignment Students should use the Mathematics summer assignment to identify subject areas that need attention in preparation for the study
More informationChapter 10. Exploring Conic Sections
Chapter 10 Exploring Conic Sections Conics A conic section is a curve formed by the intersection of a plane and a hollow cone. Each of these shapes are made by slicing the cone and observing the shape
More informationAppendix D Trigonometry
Math 151 c Lynch 1 of 8 Appendix D Trigonometry Definition. Angles can be measure in either degree or radians with one complete revolution 360 or 2 rad. Then Example 1. rad = 180 (a) Convert 3 4 into degrees.
More informationMAC Module 1 Trigonometric Functions. Rev.S08
MAC 1114 Module 1 Trigonometric Functions Learning Objectives Upon completing this module, you should be able to: 1. Use basic terms associated with angles. 2. Find measures of complementary and supplementary
More informationby Kevin M. Chevalier
Precalculus Review Handout.4 Trigonometric Functions: Identities, Graphs, and Equations, Part I by Kevin M. Chevalier Angles, Degree and Radian Measures An angle is composed of: an initial ray (side) -
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 informationTrigonometry Review Day 1
Name Trigonometry Review Day 1 Algebra II Rotations and Angle Terminology II Terminal y I Positive angles rotate in a counterclockwise direction. Reference Ray Negative angles rotate in a clockwise direction.
More informationDay 4 Trig Applications HOMEWORK
Day 4 Trig Applications HOMEWORK 1. In ΔABC, a = 0, b = 1, and mc = 44º a) Find the length of side c to the nearest integer. b) Find the area of ΔABC to the nearest tenth.. In ΔABC, ma = 50º, a = 40, b
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 informationSec 4.1 Trigonometric Identities Basic Identities. Name: Reciprocal Identities:
Sec 4. Trigonometric Identities Basic Identities Name: Reciprocal Identities: Quotient Identities: sin csc cos sec csc sin sec cos sin tan cos cos cot sin tan cot cot tan Using the Reciprocal and Quotient
More information