# Multiple Choice Questions Circle the letter of the correct answer. 7 points each. is:

Size: px
Start display at page:

Download "Multiple Choice Questions Circle the letter of the correct answer. 7 points each. is:"

Transcription

1 This Math 114 final exam was administered in the Fall of 008. This is a sample final exam. The problems are not exhaustive. Be prepared for ALL CONCEPTS for the actual final exam. Multiple Choice Questions Circle the letter of the correct answer. 7 points each The exact value of tan a) 0 b) is: c) 1 d) e) f) The exact value of sin 1 1 is: a) b) c) 6 d) 5 6 e) 5 f) For y = 4tan x, two consecutive vertical asymptotes are: a) x = 0, x = b) x =, x c) x =, x = d) x =, x = e) x = 7, x = 6 6 f) None of these. 4. The rectangular coordinates, converted to polar coordinates are: a), 4 b), 4 c), 4 5 d), 4 7 e), 4 f) None of these. 1

2 5. The exact value of csc 7 a) b) c) is: d) e) f) 6. A medical helicopter is 10 miles due south and 15 miles due east of a hospital. If the pilot wants to travel directly to the hospital, what bearing should be taken? a) S1.45 E b) S7.1 E c) N1.45 W d) N7.1 W e) N81 W f) N8.87 W g) N88.55 W h) N89.86 W 7. For an object in simple harmonic motion given by the model d 5 sin( 4t) where d is in feet and t is in seconds, the maximum displacement (in feet) and the frequency (in oscillations per second) of the object are (respectively): a) 5, 1 d) 5, 1 b) 5, c) 5, 4 e) 5, f) 5, 4 8. Find the exact value of the arclength of a circle with central angle 100 and diameter 4 feet: 18 a) feet 5 0 d) feet 9 10 b) feet c) feet 9 e) 00 feet f) 400 feet 9. The polar equation 4 r in rectangular form is: sec a) r = 4x b) r = 4y c) r 4 x d) r 4 y e) x y 4 x f) x y 4 y g) x y 16 x

3 Open-ended Questions Points for each question are labeled. Show ALL of your work. Give EXACT answers when requested. 10. (16 points) Given: a =. inches = 4 = 6 (a) Solve the triangle. Provide ±0.01 decimal place accuracy on solution. (b) Find the area of the triangle.

4 11. (18 points) For the given graph, write the function f ( x) A sin x B and find the following: [ x-scale and y-scale is 1.] 9 1 A = B = = = Amplitude Period Phase Shift Range (in interval notation) Function f ( x) = 4

5 1. (1 points) Verify the trigonometric identity. Show every step. Work going DOWN. Work on ONE side only: tan csc x x csc x cos( x) 5

6 1. (8 points) PLOT and label the following polar coordinates. CONVERT the point from polar to EXACT rectangular coordinates. 1 POLAR TO RECTANGULAR 5,, 14. (1 points) Find the EXACT value. Show all work including reference triangle. csc tan

7 15. (10 points) Find all solutions for in 0,. Give exact solutions, where possible. Otherwise, provide ± decimal place accuracy. csc 7 cot (10 points) Find all GENERAL solutions for θ in radian measure. Give EXACT algebraic solutions only. cos (sin 5 1) 0 7

8 17. (18 points) Given: sec α = 17 and 0 8 sin tan 15 and Find the EXACT value of: [Show all work and reference triangles.] a) sin b) cos 8

9 18. (15 points) A ship travels 58 miles due east then adjusts its course to N7 E. After traveling 89 miles in this direction, how far is the ship from its point of departure? [Include a labeled illustration as part of your solution, showing given bearing.] Solution should have ± 0.01 decimal place accuracy.] 9

10 19. (18 points) A woman entering an outside glass elevator on the ground floor of a hotel glances up to the top of the building across the street and notices the angle of elevation is 48. She rides the elevator up three floors (60 feet) and finds the angle of elevation to the top of the building across the street is. How tall is the building across the street? [Include a labeled illustration. Solution should have ± 0.01 decimal place accuracy.] 10

11 Math 114 Final Exam Monday, December 8, 008 Section # Name PID # FORMULA SHEET (Sum, Difference, Double and Half Angle Formulas Only) cos cos cos sin sin sin sin cos cos sin cos 1 cos tan tan tan 1 tan tan sin 1 cos sin cos sin cos cos sin tan = 1 cos sin = sin 1 cos 1 sin tan cos 1 tan 1 tan 11

### Plane 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

### PART 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.

### Youngstown 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

### MULTIPLE 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

### PART 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

### MATH 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

### 1) 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

### PLANE 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

### 4.8. Solving Problems with Trigonometry. Copyright 2011 Pearson, Inc.

4.8 Solving Problems with Trigonometry Copyright 2011 Pearson, Inc. What you ll learn about More Right Triangle Problems Simple Harmonic Motion and why These problems illustrate some of the better- known

### Precalculus CP Final Exam Review. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Precalculus CP Final Eam Review Name Date: / / MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Convert the angle in degrees to radians. Epress answer

### MA 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

### Find 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.

### MATH 229 TRIGONOMETRY. COURSE PACK (Fall 2018) Mark Turner Mathematics Division Cuesta College

MATH 9 TRIGONOMETRY COURSE PACK (Fall 08) Mark Turner Mathematics Division Cuesta College Angles and Triangles. Find the complement and supplement of 60. Complement = Supplement =. Use the Pythagorean

### SENIOR HIGH MATH LEAGUE April 24, GROUP IV Emphasis on TRIGONOMETRY

SENIOR HIGH MATH LEAGUE TEST A Write all radical expressions in simplified form and unless otherwise stated give exact answers. 1. Give the exact value for each of the following where the angle is given

### 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.

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

### High School MATHEMATICS Trigonometry

High School MATHEMATICS Trigonometry Curriculum Curriculum Map USD 457 Math Framework Performance/Open-Ended Response Assessments o First Semester (Tasks 1-3) o Second Semester (Tasks 1-4) Available on

### MULTIPLE 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)

### PRECALCULUS 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

### MATH 1113 Practice Test 5 SPRING 2016

MATH 1113 Practice Test 5 SPRING 016 1. Solve the right triangle given that 37 and b = 4. (find all the missing parts) Find the area. Solve the right triangle given that 16 and a = 31. (find all the missing

### Advanced 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

### Reciprocal Identities Quotient Identities Pythagorean Identities

2 Precalculus Review Sheet 4.2 4.4 Fundamental Identities: Reciprocal Identities Quotient Identities Pythagorean Identities = csc! cos! = tan! sin2! + cos 2! = cos! = sec! cos! = cot! tan2! + = sec 2!

### untitled 1. Unless otherwise directed, answers to this question may be left in terms of π.

Name: ate:. Unless otherwise directed, answers to this question may be left in terms of π. a) Express in degrees an angle of π radians. b) Express in radians an angle of 660. c) rod, pivoted at one end,

### Triangle 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

### Unit 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(

### Graphing 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:

### C. HECKMAN TEST 2A SOLUTIONS 170

C HECKMN TEST SOLUTIONS 170 (1) [15 points] The angle θ is in Quadrant IV and tan θ = Find the exact values of 5 sin θ, cos θ, tan θ, cot θ, sec θ, and csc θ Solution: point that the terminal side of the

### MATH 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:

### 5.5 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

### Trigonometric 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,

### Pre-Calculus Right Triangle Trigonometry Review Name Dec π

Pre-Calculus Right Triangle Trigonometry Review Name Dec 201 Convert from Radians to Degrees, or Degrees to Radians 7π 1. 0 2.. 1. 11π. Find the si trig functions of θ. If sin θ =, find the other five

### SHORT 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

### 5-2 Verifying Trigonometric Identities

5- Verifying Trigonometric Identities Verify each identity. 1. (sec 1) cos = sin 3. sin sin 3 = sin cos 4 5. = cot 7. = cot 9. + tan = sec Page 1 5- Verifying Trigonometric Identities 7. = cot 9. + tan

### Trigonometry 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

### MATH 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

### Unit 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

### Basic 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

### MIDTERM 3 PART 1 (CHAPTER 4) INTRODUCTION TO TRIGONOMETRY; MATH 141 FALL 2018 KUNIYUKI 150 POINTS TOTAL: 30 FOR PART 1, AND 120 FOR PART

Math 141 Name: MIDTERM PART 1 (CHAPTER 4) INTRODUCTION TO TRIGONOMETRY; MATH 141 FALL 2018 KUNIYUKI 150 POINTS TOTAL: 0 FOR PART 1, AND 120 FOR PART 2 Show all work, simplify as appropriate, and use good

### Common 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

### MATH 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

### Part I. There are 8 problems in Part I, each worth 5 points. No partial credit will be given, so be careful. Circle the correct answer.

Math 109 Final Final Exam-Spring 2018 Page 1 Part I. There are 8 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

### Trigonometry Curriculum Guide Scranton School District Scranton, PA

Trigonometry Scranton School District Scranton, PA Trigonometry Prerequisite: Algebra II, Geometry, Algebra I Intended Audience: This course is designed for the student who has successfully completed Algebra

### Review 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,

### Warm-Up: Final Review #1. A rectangular pen is made from 80 feet of fencing. What is the maximum area the pen can be?

Warm-Up: Final Review #1 A rectangular pen is made from 80 feet of fencing. What is the maximum area the pen can be? Warm-Up: Final Review #2 1) Find distance (-2, 4) (6, -3) 2) Find roots y = x 4-6x 2

### 1. (10 pts.) Find and simplify the difference quotient, h 0for the given function

MATH 1113/ FALL 016 FINAL EXAM Section: Grade: Name: Instructor: f ( x h) f ( x) 1. (10 pts.) Find and simplify the difference quotient, h 0for the given function h f ( x) x 5. (10 pts.) The graph of the

### Section 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

### Convert the angle to radians. Leave as a multiple of π. 1) 36 1) 2) 510 2) 4) )

MAC Review for Eam Name Convert the angle to radians. Leave as a multiple of. ) 6 ) ) 50 ) Convert the degree measure to radians, correct to four decimal places. Use.6 for. ) 0 9 ) ) 0.0 ) Convert the

### 5-2 Verifying Trigonometric Identities

Verify each identity 1 (sec 1) cos = sin sec (1 cos ) = tan 3 sin sin cos 3 = sin 4 csc cos cot = sin 4 5 = cot Page 1 4 5 = cot 6 tan θ csc tan = cot 7 = cot 8 + = csc Page 8 = csc + 9 + tan = sec 10

### Santiago AP Calculus AB/BC Summer Assignment 2018 AB: complete problems 1 64, BC: complete problems 1 73

Santiago AP Calculus AB/BC Summer Assignment 2018 AB: complete problems 1 64, BC: complete problems 1 73 AP Calculus is a rigorous college level math course. It will be necessary to do some preparatory

### Math 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

### MATH 122 Final Exam Review Precalculus Mathematics for Calculus, 7 th ed., Stewart, et al

MATH Final Eam Review Precalculus Mathematics for Calculus, 7 th ed., Stewart, et al.. Mark the point determined by on the unit circle... Sketch a graph of y = sin( ) by hand... Find the amplitude, period,

### 1. Determine the remaining sides and angles of the triangle ABC. Show all work and / or support your answer.

Trigonometry Final Exam Review: Chapters 7, 8 Chapter 7: Applications of Trigonometry and Vectors 1. Determine the remaining sides and angles of the triangle ABC. 2. Determine the remaining sides and angles

### Pre-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,

### 4-6 Inverse Trigonometric Functions

Find the exact value of each expression, if it exists. 29. The inverse property applies, because lies on the interval [ 1, 1]. Therefore, =. 31. The inverse property applies, because lies on the interval

### Chapter 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

### RELEASED. Student Booklet. Precalculus. Fall 2015 NC Final Exam. Released Items

Released Items Public Schools of North arolina State oard of Education epartment of Public Instruction Raleigh, North arolina 27699-6314 Fall 2015 N Final Exam Precalculus Student ooklet opyright 2015

### to 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

### SENIOR HIGH MATH LEAGUE April 24, 2001 SECTION I: ONE POINT EACH

GROUP V OPEN DIVISION TEST A Unless otherwise stated give exact answers. 1. Find the quotient when 8x 3 +1 is divided by 2 x + 1. 2. Given f ( x) = 5x 2b while g (x) = 4bx. If f (g(1)) = 36, what is g

### Semester Exam Review. 1. Give a real life example of a situation that can be modeled with a periodic function.

Trigonometry Semester Exam Review Name: 1. Give a real life example of a situation that can be modeled with a periodic function.. As a child goes up and down on a seesaw, his or her distance form the ground

### You found and graphed the inverses of relations and functions. (Lesson 1-7)

You found and graphed the inverses of relations and functions. (Lesson 1-7) LEQ: How do we evaluate and graph inverse trigonometric functions & find compositions of trigonometric functions? arcsine function

### 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

### Important. 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

### Review Notes for the Calculus I/Precalculus Placement Test

Review Notes for the Calculus I/Precalculus Placement Test Part 9 -. Degree and radian angle measures a. Relationship between degrees and radians degree 80 radian radian 80 degree Example Convert each

### Solving Trigonometric Equations

OpenStax-CNX module: m49398 1 Solving Trigonometric Equations OpenStax College This work is produced by OpenStax-CNX and licensed under the Creative Commons Attribution License 4.0 In this section, you

### Mid-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

### Exercise 1. Exercise 2. MAT 012 SS218 Worksheet 9 Sections Name: Consider the triangle drawn below. C. c a. A b

Consider the triangle drawn below. C Exercise 1 c a A b B 1. Suppose a = 5 and b = 12. Find c, and then find sin( A), cos( A), tan( A), sec( A), csc( A), and cot( A). 2. Now suppose a = 10 and b = 24.

### Multiple Angle and Product-to-Sum Formulas. Multiple-Angle Formulas. Double-Angle Formulas. sin 2u 2 sin u cos u. 2 tan u 1 tan 2 u. tan 2u.

3330_0505.qxd 1/5/05 9:06 AM Page 407 Section 5.5 Multiple-Angle and Product-to-Sum Formulas 407 5.5 Multiple Angle and Product-to-Sum Formulas What you should learn Use multiple-angle formulas to rewrite

### 6. Write the polynomial function of least degree & with integer coefficients if the zeros occur at 6 and i.

MIDTERM REVIEW PACKET IM3H For questions 1-, perform the given operation. Leave your answers as factored as possible. 6x 5x 4 x 4x 3 1.. 3 4 1 x 17x 8 1x 5x x x 4 x x For questions 3-5, find all the zeros

### CHAPTER 40 CARTESIAN AND POLAR COORDINATES

CHAPTER 40 CARTESIAN AND POLAR COORDINATES EXERCISE 169 Page 462 1. Express (3, 5) as polar coordinates, correct to 2 decimal places, in both degrees and in From the diagram, r = 32 + 52 = 5.83 y and 5

### Syllabus Objective: 3.1 The student will solve problems using the unit circle.

Precalculus Notes: Unit 4 Trigonometr Sllabus Objective:. The student will solve problems using the unit circle. Review: a) Convert. hours into hours and minutes. Solution: hour + (0.)(60) = hour and minutes

### College Pre Calculus A Period. Weekly Review Sheet # 1 Assigned: Monday, 9/9/2013 Due: Friday, 9/13/2013

College Pre Calculus A Name Period Weekly Review Sheet # 1 Assigned: Monday, 9/9/013 Due: Friday, 9/13/013 YOU MUST SHOW ALL WORK FOR EVERY QUESTION IN THE BOX BELOW AND THEN RECORD YOUR ANSWERS ON THE

### Section 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

### A 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

### Packet Unit 5 Trigonometry Honors Math 2 17

Packet Unit 5 Trigonometry Honors Math 2 17 Homework Day 12 Part 1 Cumulative Review of this unit Show ALL work for the following problems! Use separate paper, if needed. 1) If AC = 34, AB = 16, find sin

### Checkpoint 1 Define Trig Functions Solve each right triangle by finding all missing sides and angles, round to four decimal places

Checkpoint 1 Define Trig Functions Solve each right triangle by finding all missing sides and angles, round to four decimal places. 1.. B P 10 8 Q R A C. Find the measure of A and the length of side a..

### Catholic Central High School

Catholic Central High School Algebra II Practice Examination II Instructions: 1. Show all work on the test copy itself for every problem where work is required. Points may be deducted if insufficient or

### Trigonometry Final Review Exercises

1 The exam will last 2 hours and will be entirely short answer. Be sure to provide adequate written work to justify your answers in order to receive full credit. You will be provided with a basic trig

### Semester 2 Review Units 4, 5, and 6

Precalculus Semester 2 Review Units 4, 5, and 6 NAME: Period: UNIT 4 Simplify each expression. 1) (sec θ tan θ)(1 + tan θ) 2) cos θ sin 2 θ 1 3) 1+tan θ 1+cot θ 4) cos 2θ cosθ sin θ 5) sec 2 x sec 2 x

### Trigonometry 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.

### Math Handbook of Formulas, Processes and Tricks. Trigonometry

Math Handbook of Formulas, Processes and Tricks (www.mathguy.us) Trigonometry Prepared by: Earl L. Whitney, FSA, MAAA Version 2.1 April 10, 2017 Copyright 2012 2017, Earl Whitney, Reno NV. All Rights Reserved

### Math B Regents Exam 0606 Page 1

Math B Regents Exam 0606 Page 1 1. 060601b, P.I. A.G.3 Each graph below represents a possible relationship between temperature and pressure. Which graph does not represent a function? [A] [B] 4. 060604b,

### Circle the item below that identifies your workshop section: Bailey Dambrun Burke Mullally 10:40-11:47 MWF 12:00-1:07 MWF 1:20-2:27 MWF 1:20-2:27 MWF

MTH 11 Final Exam Name April 2, 212 Directions: Show all work for full credit. Books and notes are not allowed on this exam. You may use a calculator, but if a problem asks for an exact answer, you may

### : 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

### Name: Block: What I can do for this unit:

Unit 8: Trigonometry Student Tracking Sheet Math 10 Common Name: Block: What I can do for this unit: After Practice After Review How I Did 8-1 I can use and understand triangle similarity and the Pythagorean

### Algebra 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

### DAY 1 - GEOMETRY FLASHBACK

DAY 1 - GEOMETRY FLASHBACK Sine Opposite Hypotenuse Cosine Adjacent Hypotenuse sin θ = opp. hyp. cos θ = adj. hyp. tan θ = opp. adj. Tangent Opposite Adjacent a 2 + b 2 = c 2 csc θ = hyp. opp. sec θ =

### Pre-Calc Trig ~1~ NJCTL.org. Unit Circle Class Work Find the exact value of the given expression. 7. Given the terminal point ( 3, 2 10.

Unit Circle Class Work Find the exact value of the given expression.. cos π. tan 5π 6. sin 7π 5. cot 5π. sec π 6. csc 9π 7. Given the terminal point (, 0 ) find tanθ 7 tan θ = 0 7 8. Given the terminal

### CLEP 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..

### PreCalculus Review for Math 400

PreCalculus Review for Math.) Completely factor..) For the function.) For the functions f ( ), evaluate ( ) f. f ( ) and g( ), find and simplify f ( g( )). Then, give the domain of f ( g( ))..) Solve.

### Section 10.1 Polar Coordinates

Section 10.1 Polar Coordinates Up until now, we have always graphed using the rectangular coordinate system (also called the Cartesian coordinate system). In this section we will learn about another system,

### Unit 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:

### HONORS PRECALCULUS Prove the following identities- x x= x x 1.) ( ) 2 2.) 4.) tan x 1 cos x 6.)

HONORS PRECALCULUS Prove the following identities- 1.) ( ) cosx sinx = 1 sinxcosx.) cos x tan x+ sec x= 1 sinx 3.) 1 + 1 = csc x 1 cos x 1+ cos x 4.) sec x + 1 sin x = tan x 1 cos x 5.) cot cos cos cot

### Day 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

### 1. Be sure to complete the exploration before working on the rest of this worksheet.

PreCalculus Worksheet 4.1 1. Be sure to complete the exploration before working on the rest of this worksheet.. The following angles are given to you in radian measure. Without converting to degrees, draw

### sin30 = 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

### You are not expected to transform y = tan(x) or solve problems that involve the tangent function.

In this unit, we will develop the graphs for y = sin(x), y = cos(x), and later y = tan(x), and identify the characteristic features of each. Transformations of y = sin(x) and y = cos(x) are performed and

### Math Analysis Final Exam Review. Chapter 1 Standards

Math Analysis Final Exam Review Chapter 1 Standards 1a 1b 1c 1d 1e 1f 1g Use the Pythagorean Theorem to find missing sides in a right triangle Use the sine, cosine, and tangent functions to find missing

### Unit 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

### Date Lesson Text TOPIC Homework. Getting Started Pg. 314 # 1-7. Radian Measure and Special Angles Sine and Cosine CAST

UNIT 5 TRIGONOMETRIC FUNCTIONS Date Lesson Text TOPIC Homework Oct. 0 5.0 (50).0 Getting Started Pg. # - 7 Nov. 5. (5). Radian Measure Angular Velocit Pg. 0 # ( 9)doso,,, a Nov. 5 Nov. 5. (5) 5. (5)..