Algebra and Trig. I. P=(x,y) 1 1. x x
|
|
- Berniece Atkinson
- 5 years ago
- Views:
Transcription
1 Algebra and Trig. I 4.3 Right Angle Trigonometry y P=(x,y) y P=(x,y) 1 1 y x x x We construct a right triangle by dropping a line segment from point P perpendicular to the x-axis. So now we can view as the measure of an acute angle in the right triangle. 1 P a g e
2 SOHCAHTOA (pronounced so-cah-tow-ah) Pythagorean Theorem a b c 2 P a g e
3 Example Find the value of each of the six trigonometric functions of given the following figure. c a=5 b=12 Example Find the value of each of the six trigonometric functions of given the following figure. c=3 a=1 b 3 P a g e
4 Special Triangle Relationships An equilateral triangle is a triangle with three equal sides. The three angles of an equilateral triangle are also equal. Each angle measures 60. An isosceles triangle is a triangle with exactly two equal sides. The angles opposite these equal sides are also equal. A scalene triangle is a triangle with all three sides unequal. A triangle is an isosceles right triangle. The two base angles are each 45, and the last angle is 90. The sum of the angles of a triangle is Properties of a triangle. A triangle is an equilateral triangle cut in half. An equilateral triangle has angle measures , therefore when we divide the top angle in half that measure becomes 30, the altitude creates a 90 angle at the bottom P a g e 1
5 So how to find the values of the trigonometric functions at So how to find the values of the trigonometric functions at So how to find the values of the trigonometric functions at 5 P a g e
6 Trigonometric Functions and Complements Two positive angles are complements if the sum of their angles is. For example 70 and 20 are complements because =90. c b 90- a The figure to the left shows a right triangle. Because the sum of the angles of any triangle is 180, in a right triangle the sum of the acute angles is 90, thus the acute angles are complements. If one acute angle is the other must be 90 - From above we can conclude that. If two angles are complements then the sine of one equals the cosine of the other. Because of this relationship the sine and cosine functions are called confunctions of each other. (The name cosine is a shortened form of the phrase complement s sine.) 6 P a g e
7 Any pair of trig. functions f and g for which confunctions. are called Confunction Identities The value of a trigonometric function of is equal to the confunction of the complement of. Confunctions of complementary angles are equal. Example Find a confunction with the same value as the given expression P a g e
8 Applications Line of Sight above Observer Angle of elevation Angle of depression Horizontal Line of Sight below Observer The angle of elevation is the angle from the horizontal line to the line of sight above the observer The angle of depression is the angle from the horizontal line to the line of sight below the observer Example A tower that is 125 feet tall casts a shadow 172 feet. Find the angle of elevation. 8 P a g e
9 Example The irregular shape is a lake. The distance across the lake is unknown. To find the distance a surveyor took the measurement shown. What is the distance across the lake? (=22 ) a 300 yards 9 P a g e
North Carolina Math 2 Transition Edition Unit 5 Assessment: Trigonometry
Name: Class: _ Date: _ North Carolina Math 2 Transition Edition Unit 5 Assessment: Trigonometry Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the
More informationTrigonometric Functions. Copyright Cengage Learning. All rights reserved.
4 Trigonometric Functions Copyright Cengage Learning. All rights reserved. 4.3 Right Triangle Trigonometry Copyright Cengage Learning. All rights reserved. What You Should Learn Evaluate trigonometric
More information: SINE, COSINE, & TANGENT RATIOS
Geometry Notes Packet Name: 9.2 9.4: SINE, COSINE, & TANGENT RATIOS Trigonometric Ratios A ratio of the lengths of two sides of a right triangle. For any acute angle, there is a leg Opposite the angle
More informationSHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
MATH 116 Test Review sheet SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 1) Find the complement of an angle whose measure
More informationCourse Learning Objectives: Demonstrate an understanding of trigonometric functions and their applications.
Right Triangle Trigonometry Video Lecture Section 8.1 Course Learning Objectives: Demonstrate an understanding of trigonometric functions and their applications. Weekly Learning Objectives: 1)Find the
More informationGeometry Warm Up Right Triangles Day 8 Date
Geometry Warm Up Right Triangles Day 8 Name Date Questions 1 4: Use the following diagram. Round decimals to the nearest tenth. P r q Q p R 1. If PR = 12 and m R = 19, find p. 2. If m P = 58 and r = 5,
More informationWarm Up 1. What is the third angle measure in a triangle with angles measuring 65 and 43? 72
Warm Up 1. What is the third angle measure in a triangle with angles measuring 65 and 43? 72 Find each value. Round trigonometric ratios to the nearest hundredth and angle measures to the nearest degree.
More informationThe Primary Trigonometric Ratios Word Problems
The Primary Trigonometric Ratios Word Problems A. Determining the measures of the sides and angles of right triangles using the primary ratios When we want to measure the height of an inaccessible object
More informationName Date Period Notes Formal Geometry Chapter 8 Right Triangles and Trigonometry 8.1 Geometric Mean. A. Definitions: 1.
Name Date Period Notes Formal Geometry Chapter 8 Right Triangles and Trigonometry 8.1 Geometric Mean A. Definitions: 1. Geometric Mean: 2. Right Triangle Altitude Similarity Theorem: If the altitude is
More informationTrigonometric ratios:
0 Trigonometric ratios: The six trigonometric ratios of A are: Sine Cosine Tangent sin A = opposite leg hypotenuse adjacent leg cos A = hypotenuse tan A = opposite adjacent leg leg and their inverses:
More informationGeometry Right Triangles and Trigonometry
Geometry Right Triangles and Trigonometry Day Date lass Homework Th 2/16 F 2/17 N: Special Right Triangles & Pythagorean Theorem Right Triangle & Pythagorean Theorem Practice Mid-Winter reak WKS: Special
More information8.6 Inverse Trigonometric Ratios
www.ck12.org Chapter 8. Right Triangle Trigonometry 8.6 Inverse Trigonometric Ratios Learning Objectives Use the inverse trigonometric ratios to find an angle in a right triangle. Solve a right triangle.
More informationLesson 1: Trigonometry Angles and Quadrants
Trigonometry Lesson 1: Trigonometry Angles and Quadrants An angle of rotation can be determined by rotating a ray about its endpoint or. The starting position of the ray is the side of the angle. The position
More information~ 1 ~ Geometry 2 nd Semester Review Find the value for the variable for each of the following situations
Geometry nd Semester Review 018 Find the value for the variable for each of the following situations. 7. 400 m 1. 7 8. y. 8.9 cm 0 0 9.. 19 6 60 1 11 10. 45 4. 58 5 11. 5. 11 6. 18 1 slide 4.1 meters long
More informationPre-AP Geometry 8-4 Study Guide: Angles of Elevation and Depression (pp ) Page! 1 of! 8
Page! 1 of! 8 Attendance Problems. 1. Identify the the pair of alternate interior angles. 2. Use a calculator to find! tan 30 to the nearest ten-thousandth. 3. Solve! tan 54 = 2500 Round your answer to
More informationChapter 4 Trigonometric Functions
SECTION 4.1 Special Right Triangles and Trigonometric Ratios Chapter 4 Trigonometric Functions Section 4.1: Special Right Triangles and Trigonometric Ratios Special Right Triangles Trigonometric Ratios
More informationGeometry Note Cards EXAMPLE:
Geometry Note Cards EXAMPLE: Lined Side Word and Explanation Blank Side Picture with Statements Sections 12-4 through 12-5 1) Theorem 12-3 (p. 790) 2) Theorem 12-14 (p. 790) 3) Theorem 12-15 (p. 793) 4)
More informationSquare Root Functions 10.1
Square Root Functions 10.1 Square Root Function contains the square root of the variable. Parent Function: f ( x) = Type of Graph: Curve Domain: x 0 Range: y 0 x Example 1 Graph f ( x) = 2 x and state
More information2. Pythagorean Theorem:
Chapter 4 Applications of Trigonometric Functions 4.1 Right triangle trigonometry; Applications 1. A triangle in which one angle is a right angle (90 0 ) is called a. The side opposite the right angle
More informationAssignment 1 and 2: Complete practice worksheet: Simplifying Radicals and check your answers
Geometry 0-03 Summary Notes Right Triangles and Trigonometry These notes are intended to be a guide and a help as you work through Chapter 8. These are not the only thing you need to read, however. Rely
More informationUNIT 7: TRIGONOMETRY.
UNIT 7: TRIGONOMETRY. Trigonometry: Trigonometry (from Greek trigonom triangle and metron measure ) is a branch of mathematics that studies triangles and the relationships between their sides and their
More informationMATH 2412 Sections Fundamental Identities. Reciprocal. Quotient. Pythagorean
MATH 41 Sections 5.1-5.4 Fundamental Identities Reciprocal Quotient Pythagorean 5 Example: If tanθ = and θ is in quadrant II, find the exact values of the other 1 trigonometric functions using only fundamental
More informationGeometry. of Right Triangles. Pythagorean Theorem. Pythagorean Theorem. Angles of Elevation and Depression Law of Sines and Law of Cosines
Geometry Pythagorean Theorem of Right Triangles Angles of Elevation and epression Law of Sines and Law of osines Pythagorean Theorem Recall that a right triangle is a triangle with a right angle. In a
More informationJan 1 4:08 PM. We write this in a shorter manner for simplicity. leg
Review Pythagorean Theorem Jan 1 4:08 PM We write this in a shorter manner for simplicity. leg hyp leg or a c b Note, the last statement can be misleading if the letters used are not in the correct position.
More informationGeometry Unit 7 - Notes Right Triangles and Trigonometry
Geometry Unit 7 - Notes Right Triangles and Trigonometry Review terms: 1) right angle ) right triangle 3) adjacent 4) Triangle Inequality Theorem Review topic: Geometric mean a = = d a d Syllabus Objective:
More informationT.4 Applications of Right Angle Trigonometry
424 section T4 T.4 Applications of Right Angle Trigonometry Solving Right Triangles Geometry of right triangles has many applications in the real world. It is often used by carpenters, surveyors, engineers,
More informationRight Triangle Trigonometry
Section 6.4 OBJECTIVE : Right Triangle Trigonometry Understanding the Right Triangle Definitions of the Trigonometric Functions otenuse osite side otenuse acent side acent side osite side We will be concerned
More information15 x. Substitute. Multiply. Add. Find the positive square root.
hapter Review.1 The Pythagorean Theorem (pp. 3 70) Dynamic Solutions available at igideasmath.com Find the value of. Then tell whether the side lengths form a Pythagorean triple. c 2 = a 2 + b 2 Pythagorean
More informationNew Jersey Center for Teaching and Learning. Progressive Mathematics Initiative
Slide 1 / 240 New Jersey Center for Teaching and Learning Progressive Mathematics Initiative This material is made freely available at www.njctl.org and is intended for the non-commercial use of students
More informationDay 6: Angles of Depression and Elevation. Unit 5: Trigonometric Functions
+ Day 6: Angles of Depression and Elevation Unit 5: Trigonometric Functions Warm Up + n Find the missing side length 1) 2) n Find the missing angle 10 minutes 3) 4) End + Homework Check + Today s Objective
More informationThe graph of a proportional relation always contains the origin and has a slope equal to the constant of proportionality.
Chapter 11.1 Ratios and Rates A ratio is a comparison of two numbers, a and b, by division. The numbers a and b are called terms of the ratio. A ratio can be expressed in three different ways. 1. Word
More informationAlgebra 1B. Unit 9. Algebraic Roots and Radicals. Student Reading Guide. and. Practice Problems
Name: Date: Period: Algebra 1B Unit 9 Algebraic Roots and Radicals Student Reading Guide and Practice Problems Contents Page Number Lesson 1: Simplifying Non-Perfect Square Radicands 2 Lesson 2: Radical
More informationBasic Trigonometry. Trigonometry deals with the relations between the sides and angles of triangles.
Basic Trigonometry Trigonometry deals with the relations between the sides and angles of triangles. A triangle has three sides and three angles. Depending on the size of the angles, triangles can be: -
More informationAssumption High School BELL WORK. Academic institution promoting High expectations resulting in Successful students
BELL WORK Geometry 2016 2017 Day 51 Topic: Chapter 8.3 8.4 Chapter 8 Big Ideas Measurement Some attributes of geometric figures, such as length, area, volume, and angle measure, are measurable. Units are
More informationGeometry Rules! Chapter 8 Notes
Geometr Rules! Chapter 8 Notes - 1 - Notes #6: The Pthagorean Theorem (Sections 8.2, 8.3) A. The Pthagorean Theorem Right Triangles: Triangles with right angle Hpotenuse: the side across from the angle
More informationGeometry. Trigonometry of Right Triangles. Slide 1 / 240. Slide 2 / 240. Slide 3 / 240
New Jersey enter for Teaching and Learning Slide 1 / 240 Progressive Mathematics Initiative This material is made freely available at www.njctl.org and is intended for the non-commercial use of students
More informationTrigonometry. General Outcome: Develop trigonometric reasoning.
Math 20-1 Chapter 2 Trigonometry General Outcome: Develop trigonometric reasoning. Specific Outcomes: T1. Demonstrate an understanding of angles in standard position [0 to 360 ]. [R, V] T2. Solve problems,
More information1. For Cosine Rule of any triangle ABC, b² is equal to A. a² - c² 4bc cos A B. a² + c² - 2ac cos B C. a² - c² + 2ab cos A D. a³ + c³ - 3ab cos A
1. For Cosine Rule of any triangle ABC, b² is equal to A. a² - c² 4bc cos A B. a² + c² - 2ac cos B C. a² - c² + 2ab cos A D. a³ + c³ - 3ab cos A 2. For Cosine Rule of any triangle ABC, c² is equal to A.
More information1.3 Basic Trigonometric Functions
www.ck1.org Chapter 1. Right Triangles and an Introduction to Trigonometry 1. Basic Trigonometric Functions Learning Objectives Find the values of the six trigonometric functions for angles in right triangles.
More informationCK- 12 Algebra II with Trigonometry Concepts 1
1.1 Pythagorean Theorem and its Converse 1. 194. 6. 5 4. c = 10 5. 4 10 6. 6 5 7. Yes 8. No 9. No 10. Yes 11. No 1. No 1 1 1. ( b+ a)( a+ b) ( a + ab+ b ) 1 1 1 14. ab + c ( ab + c ) 15. Students must
More informationBrunswick School Department Honors Geometry Unit 6: Right Triangles and Trigonometry
Understandings Questions Knowledge Vocabulary Skills Right triangles have many real-world applications. What is a right triangle? How to find the geometric mean of two numbers? What is the Pythagorean
More information8 Right Triangle Trigonometry
www.ck12.org CHAPTER 8 Right Triangle Trigonometry Chapter Outline 8.1 THE PYTHAGOREAN THEOREM 8.2 CONVERSE OF THE PYTHAGOREAN THEOREM 8.3 USING SIMILAR RIGHT TRIANGLES 8.4 SPECIAL RIGHT TRIANGLES 8.5
More informationPrerequisite Skills. y x =
Prerequisite Skills BLM 1 1... Solve Equations 1. Solve. 2x + 5 = 11 x 5 + 6 = 7 x 2 = 225 d) x 2 = 24 2 + 32 2 e) 60 2 + x 2 = 61 2 f) 13 2 12 2 = x 2 The Pythagorean Theorem 2. Find the measure of the
More informationUse a calculator to find the value of the expression in radian measure rounded to 2 decimal places. 1 8) cos-1 6
Math 180 - chapter 7 and 8.1-8. - New Edition - Spring 09 Name Find the value of the expression. 1) sin-1 0.5 ) tan-1-1 ) cos-1 (- ) 4) sin-1 Find the exact value of the expression. 5) sin [sin-1 (0.7)]
More information1. Make a sketch of the triangles shown below and mark on each triangle the hypotenuse, the opposite and the adjacent sides to the angle. a b c.
Chapter 16 Trigonometry Exercise 16.1 1. Make a sketch of the triangles shown below and mark on each triangle the hypotenuse, the opposite and the adjacent sides to the angle. adj 2. Use the tangent (or
More informationMATH 109 TOPIC 3 RIGHT TRIANGLE TRIGONOMETRY. 3a. Right Triangle Definitions of the Trigonometric Functions
Math 09 Ta-Right Triangle Trigonometry Review Page MTH 09 TOPIC RIGHT TRINGLE TRIGONOMETRY a. Right Triangle Definitions of the Trigonometric Functions a. Practice Problems b. 5 5 90 and 0 60 90 Triangles
More information5.1: Angles and Radian Measure Date: Pre-Calculus
5.1: Angles and Radian Measure Date: Pre-Calculus *Use Section 5.1 (beginning on pg. 482) to complete the following Trigonometry: measurement of triangles An angle is formed by two rays that have a common
More informationGeometry. Trigonometry of Right Triangles. Slide 1 / 240. Slide 2 / 240. Slide 3 / 240
New Jersey enter for Teaching and Learning Slide 1 / 240 Progressive Mathematics Initiative This material is made freely available at www.njctl.org and is intended for the non-commercial use of students
More informationUnit Circle. Return to. Contents
Unit Circle Return to Table of Contents 32 The Unit Circle The circle x 2 + y 2 = 1, with center (0,0) and radius 1, is called the unit circle. Quadrant II: x is negative and y is positive (0,1) 1 Quadrant
More informationLesson 16: Applications of Trig Ratios to Find Missing Angles
: Applications of Trig Ratios to Find Missing Angles Learning Targets I can find a missing angle in a right triangle diagram and apply this to real world situation Opening Exercise Find the shadow cast
More informationComplement Angle Relationships
We Complement Each Other! Complement Angle Relationships 8.5 Learning Goals In this lesson, you will: Explore complement angle relationships in a right triangle. Solve problems using complement angle relationships.
More informationMath 521B Trigonometry Assignment
Math 521B Trigonometry Assignment Multiple Choice Identify the choice that best completes the statement or answers the question. 1. What is the reference angle for 200 in standard position? A 100 C 20
More informationName: Period: Geometry Unit 5: Trigonometry Homework. x a = 4, b= a = 7, b = a = 6, c = a = 3, b = 7
Name: Period: Geometr Unit 5: Trigonometr Homework Section 5.1: Pthagorean Theorem Find the value of each variable or missing side. Leave answers in simplest radical form AND as a decimal rounded to the
More informationLT 2.1 Study Guide and Intervention Classifying Triangles
LT 2.1 Study Guide and Intervention Classifying Triangles Classify Triangles by Angles One way to classify a triangle is by the measures of its angles. If all three of the angles of a triangle are acute
More informationIntegrated Math II. IM2.1.2 Interpret given situations as functions in graphs, formulas, and words.
Standard 1: Algebra and Functions Students graph linear inequalities in two variables and quadratics. They model data with linear equations. IM2.1.1 Graph a linear inequality in two variables. IM2.1.2
More informationChapter 2: Trigonometry
Chapter 2: Trigonometry Section 2.1 Chapter 2: Trigonometry Section 2.1: The Tangent Ratio Sides of a Right Triangle with Respect to a Reference Angle Given a right triangle, we generally label its sides
More informationRadicals and Pythagorean Theorem Date: Per:
Math 2 Unit 7 Worksheet 1 Name: Radicals and Pythagorean Theorem Date: Per: [1-12] Simplify each radical expression. 1. 75 2. 24. 7 2 4. 10 12 5. 2 6 6. 2 15 20 7. 11 2 8. 9 2 9. 2 2 10. 5 2 11. 7 5 2
More informationOctober 15 MATH 1113 sec. 51 Fall 2018
October 15 MATH 1113 sec. 51 Fall 2018 Section 5.5: Solving Exponential and Logarithmic Equations Base-Exponent Equality For any a > 0 with a 1, and for any real numbers x and y a x = a y if and only if
More informationMPM 2DI EXAM REVIEW. Monday, June 19, :30 AM 1:00 PM * A PENCIL, SCIENTIFIC CALCULATOR AND RULER ARE REQUIRED *
NAME: MPM DI EXAM REVIEW Monday, June 19, 017 11:30 AM 1:00 PM * A PENCIL, SCIENTIFIC CALCULATOR AND RULER ARE REQUIRED * Please Note: Your final mark in this course will be calculated as the better of:
More informationTRIGONOMETRY USING THE RATIOS
TRIGONOMETRY USING THE RATIOS 2017 JCHL Paper 2 Question 8 (a) The diagram below shows two right-angled triangles, ABC and ACD. They have right angles at B and D, respectively. AB = 10, AC = 12, and AD
More informationLet be an acute angle. Use a calculator to approximate the measure of to the nearest tenth of a degree.
Ch. 9 Test - Geo H. Let be an acute angle. Use a calculator to approximate the measure of to the nearest tenth of a degree. 1. 2. 3. a. about 58.0 c. about 1.0 b. about 49.4 d. about 32.0 a. about 52.2
More informationTrigonometry. Sin θ Cos θ Tan θ Cot θ Sec θ Cosec θ. Sin = = cos = = tan = = cosec = sec = 1. cot = sin. cos. tan
Trigonometry Trigonometry is one of the most interesting chapters of Quantitative Aptitude section. Basically, it is a part of SSC and other bank exams syllabus. We will tell you the easy method to learn
More informationThe No Calculators Pages
Trigonometry Summer 2005 Name: The No Calculators Pages Instructions: See front page for general instructions. Finish this page before going to the rest. You may not return to this page once you turn on
More informationPRACTICE PROBLEMS CH 8 and Proofs
GEOM PRACTICE PROBLEMS CH 8 and Proofs Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the length of the missing side. The triangle is not drawn to
More informationCh. 2 Trigonometry Notes
First Name: Last Name: Block: Ch. 2 Trigonometry Notes 2.1 THE TANGENT RATIO 2 Ch. 2.1 HW: p. 75 #3 16, 19 4 2.2 USING THE TANGENT RATIO TO CALCULATE LENGTHS 5 Ch. 2.2 HW: p. 82 # 3 5 (a, c), #6 14 6 2.4
More informationTriangles and Vectors
Chapter 3 Triangles and Vectors As was stated at the start of Chapter 1, trigonometry had its origins in the study of triangles. In fact, the word trigonometry comes from the Greek words for triangle measurement.
More informationAlgebra II Standard Term 4 Review packet Test will be 60 Minutes 50 Questions
Algebra II Standard Term Review packet 2017 NAME Test will be 0 Minutes 0 Questions DIRECTIONS: Solve each problem, choose the correct answer, and then fill in the corresponding oval on your answer document.
More informationChapter 8 Test Wednesday 3/28
Chapter 8 Test Wednesday 3/28 Warmup Pg. 487 #1-4 in the Geo book 5 minutes to finish 1 x = 4.648 x = 40.970 x = 6149.090 x = -5 What are we learning today? Pythagoras The Rule of Pythagoras Using Pythagoras
More informationGiven an arc of length s on a circle of radius r, the radian measure of the central angle subtended by the arc is given by θ = s r :
Given an arc of length s on a circle of radius r, the radian measure of the central angle subtended by the arc is given by θ = s r : To convert from radians (rad) to degrees ( ) and vice versa, use the
More informationPre-Calc Trigonometry
Slide 1 / 207 Slide 2 / 207 Pre-Calc Trigonometry 2015-03-24 www.njctl.org Slide 3 / 207 Table of Contents Unit Circle Graphing Law of Sines Law of Cosines Pythagorean Identities Angle Sum/Difference Double
More informationName Date Trigonometry of the Right Triangle Class Work Unless otherwise directed, leave answers as reduced fractions or round to the nearest tenth.
Name Date Trigonometry of the Right Triangle Class Work Unless otherwise directed, leave answers as reduced fractions or round to the nearest tenth. 1. Evaluate the sin, cos, and tan of θ(theta). 2. Evaluate
More informationGiven an arc of length s on a circle of radius r, the radian measure of the central angle subtended by the arc is given by θ = s r :
Given an arc of length s on a circle of radius r, the radian measure of the central angle subtended by the arc is given by θ = s r : To convert from radians (rad) to degrees ( ) and vice versa, use the
More information8.5 angles of elevation and depression ink.notebook. March 05, Page 74 Page Angles of Elevation and Depression. Page 76.
8.5 angles of elevation and depression ink.notebook 65 Page 74 Page 73 8.5 Angles of Elevation and Depression Page 75 Page 76 1 Lesson Objectives Standards Lesson Notes Lesson Objectives Standards Lesson
More informationCourse End Review Grade 10: Academic Mathematics
Course End Review Grade 10: Academic Mathematics Linear Systems: 1. For each of the following linear equations place in y = mx + b format. (a) 3 x + 6y = 1 (b) 4 x 3y = 15. Given 1 x 4y = 36, state: (a)
More informationPART 1: USING SCIENTIFIC CALCULATORS (50 PTS.)
Math 141 Name: MIDTERM 4 PART 1 (CHAPTERS 5 AND 6: ANALYTIC & MISC. TRIGONOMETRY) MATH 141 SPRING 2018 KUNIYUKI 150 POINTS TOTAL: 50 FOR PART 1, AND 100 FOR PART 2 Show all work, simplify as appropriate,
More informationExercise Set 4.1: Special Right Triangles and Trigonometric Ratios
Eercise Set.1: Special Right Triangles and Trigonometric Ratios Answer the following. 9. 1. If two sides of a triangle are congruent, then the opposite those sides are also congruent. 2. If two angles
More informationPre-Calculus EOC Review 2016
Pre-Calculus EOC Review 2016 Name The Exam 50 questions, multiple choice, paper and pencil. I. Limits 8 questions a. (1) decide if a function is continuous at a point b. (1) understand continuity in terms
More information2. What are the three other angles in standard position that have a reference angle of 54? A C B D
exam unit 2 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. What is the reference angle for 15 in standard position? A 255 C 345 B 30 D 15 2. What are
More informationSHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Math 1332 Chapter 10 Review Name Solve the problem. 1) The hour hand of a clock moves from 12 to 4 oʹclock. Through how many degrees does it move? 1) Find the measure of the angle in which? appears. 2)
More informationVectors. An Introduction
Vectors An Introduction There are two kinds of quantities Scalars are quantities that have magnitude only, such as position speed time mass Vectors are quantities that have both magnitude and direction,
More informationTrigonometry of the Right Triangle Class Work
Trigonometry of the Right Triangle Class Work Unless otherwise directed, leave answers as reduced fractions or round to the nearest tenth. 1. Evaluate the sin, cos, and tan of θ(theta). 2. Evaluate the
More informationHistogram, cumulative frequency, frequency, 676 Horizontal number line, 6 Hypotenuse, 263, 301, 307
INDEX A Abscissa, 76 Absolute value, 6 7, 55 Absolute value function, 382 386 transformations of, reflection, 386 scaling, 386 translation, 385 386 Accuracy, 31 Acute angle, 249 Acute triangle, 263 Addition,
More informationsin cos 1 1 tan sec 1 cot csc Pre-Calculus Mathematics Trigonometric Identities and Equations
Pre-Calculus Mathematics 12 6.1 Trigonometric Identities and Equations Goal: 1. Identify the Fundamental Trigonometric Identities 2. Simplify a Trigonometric Expression 3. Determine the restrictions on
More informationUnit 3 Practice Test Questions Trigonometry
Unit 3 Practice Test Questions Trigonometry Multiple Choice Identify the choice that best completes the statement or answers the question. 1. How you would determine the indicated angle measure, if it
More informationSquares and Square Roots. The Pythagorean Theorem. Similar Figures and Indirect Measurement
Lesson 9-1 Lesson 9-2 Lesson 9-3 Lesson 9-4 Lesson 9-5 Lesson 9-6 Squares and Square Roots The Real Number System Triangles The Pythagorean Theorem The Distance Formula Similar Figures and Indirect Measurement
More informationName Score Period Date. m = 2. Find the geometric mean of the two numbers. Copy and complete the statement.
Chapter 6 Review Geometry Name Score Period Date Solve the proportion. 3 5 1. = m 1 3m 4 m = 2. 12 n = n 3 n = Find the geometric mean of the two numbers. Copy and complete the statement. 7 x 7? 3. 12
More informationTrigonometry Applications
Name: Date: Period Trigonometry Applications Draw a picture (if one is not provided), write an equation, and solve each problem. Round answers to the nearest hundredths. 1. A 110-ft crane set at an angle
More informationCollege Trigonometry
College Trigonometry George Voutsadakis 1 1 Mathematics and Computer Science Lake Superior State University LSSU Math 11 George Voutsadakis (LSSU) Trigonometry January 015 1 / 8 Outline 1 Trigonometric
More informationName: Period: Geometry Honors Unit 5: Trigonometry Homework. x a = 4, b= a = 7, b = a = 6, c =
Name: Period: Geometr Honors Unit 5: Trigonometr Homework Section 5.1: Pthagorean Theorem Find the value of each variable or missing side. Leave answers in simplest radical form ND as a decimal rounded
More informationContent Guidelines Overview
Content Guidelines Overview The Pearson Video Challenge is open to all students, but all video submissions must relate to set of predetermined curriculum areas and topics. In the following pages the selected
More informationCHAPTER 1. ANGLES AND BASIC TRIG
DR. YOU: 017 FALL 1 CHAPTER 1. ANGLES AND BASIC TRIG LECTURE 1-0 REVIEW EXAMPLE 1 YOUR TURN 1 Simplify the radical expression. Simplify the radical expression. (A) 108 (A) 50 First, find the biggest perfect
More information(A) (12, 5) (B) ( 8, 15) (C) (3,6) (D) (4,4)
DR. YOU: 018 FALL 1 CHAPTER 1. ANGLES AND BASIC TRIG LECTURE 1-0 REVIEW EXAMPLE 1 YOUR TURN 1 Simplify the radical expression. Simplify the radical expression. (A) 108 (A) 50 First, find the biggest perfect
More informationMath 2 Trigonometry. People often use the acronym SOHCAHTOA to help remember which is which. In the triangle below: = 15
Math 2 Trigonometry 1 RATIOS OF SIDES OF A RIGHT TRIANGLE Trigonometry is all about the relationships of sides of right triangles. In order to organize these relationships, each side is named in relation
More informationPre Calc. Trigonometry.
1 Pre Calc Trigonometry 2015 03 24 www.njctl.org 2 Table of Contents Unit Circle Graphing Law of Sines Law of Cosines Pythagorean Identities Angle Sum/Difference Double Angle Half Angle Power Reducing
More informationStudy Guide for Benchmark #1 Window of Opportunity: March 4-11
Study Guide for Benchmark #1 Window of Opportunity: March -11 Benchmark testing is the department s way of assuring that students have achieved minimum levels of computational skill. While partial credit
More informationI IV II III 4.1 RADIAN AND DEGREE MEASURES (DAY ONE) COMPLEMENTARY angles add to90 SUPPLEMENTARY angles add to 180
4.1 RADIAN AND DEGREE MEASURES (DAY ONE) TRIGONOMETRY: the study of the relationship between the angles and sides of a triangle from the Greek word for triangle ( trigonon) (trigonon ) and measure ( metria)
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. Use the appropriate identity to find the indicated function value. Rationalize the denominator,
More informationCore Mathematics 2 Trigonometry
Core Mathematics 2 Trigonometry Edited by: K V Kumaran Email: kvkumaran@gmail.com Core Mathematics 2 Trigonometry 2 1 Trigonometry Sine, cosine and tangent functions. Their graphs, symmetries and periodicity.
More informationDirections: Examine the Unit Circle on the Cartesian Plane (Unit Circle: Circle centered at the origin whose radius is of length 1)
Name: Period: Discovering the Unit Circle Activity Secondary III For this activity, you will be investigating the Unit Circle. You will examine the degree and radian measures of angles. Note: 180 radians.
More informationGeometry Similar Triangles & Trigonometry
1 Geometry Similar Triangles & Trigonometry 2015-10-22 www.njctl.org 2 Table of Contents Problem Solving with Similar Triangles click on the topic to go to that section Similar Triangles and Trigonometry
More information