MTH 133: Plane Trigonometry
|
|
|
- Domenic Sanders
- 6 years ago
- Views:
Transcription
1 MTH 133: Plane Trigonometry Radian Measure, Arc Length, and Area Angular and Linear Velocity Thomas W. Judson Department of Mathematics & Statistics Stephen F. Austin State University Fall 2017 Plane Trigonometry (MTH 133) Plane Trigonometry Notes Fall / 20 Contents I 1 2 Plane Trigonometry (MTH 133) Plane Trigonometry Notes Fall / 20
2 Course Orientation Overview Everything that you need to know about MTH 133 can be found at Our graphing calculator of choice is Desmos ( The homework system for MTH 133 is WeBWorK ( Plane Trigonometry (MTH 133) Plane Trigonometry Notes Fall / 20 Course Orientation Plane Trigonometry (MTH 133) Plane Trigonometry Notes Fall / 20
3 The Unit Circle and Radians Definition 1 The unit circle is the circle of radius one centered at the origin, or x 2 + y 2 = 1. 2 The radian measure of an angle α in the standard position is the directed length of the intercepted arc on the unit circle. Plane Trigonometry (MTH 133) Plane Trigonometry Notes Fall / 20 Plane Trigonometry (MTH 133) Plane Trigonometry Notes Fall / 20
4 Radians to Degrees and Degrees to Radians Fact Conversion from radians to degrees is based on 180 degrees = π radians. Convert each of the following from degrees to radians Plane Trigonometry (MTH 133) Plane Trigonometry Notes Fall / 20 Plane Trigonometry (MTH 133) Plane Trigonometry Notes Fall / 20
5 Arc Length of a Circle Fact The length s of an arc intercepted by a central angle of α radians on a circle of radius r is given by s = αr. 1 What is the length of an arc intercepted by α = π/4 on a circle of radius 12 feet? 2 What is the length of an arc intercepted by α = 60 on a circle of radius 2 meters? Plane Trigonometry (MTH 133) Plane Trigonometry Notes Fall / 20 Plane Trigonometry (MTH 133) Plane Trigonometry Notes Fall / 20
6 Area of a Sector of a Circle Fact The area A of a sector with a central angle of α radians on a circle of radius r is given by A = αr What is the area of a sector of a circle with central angle by α = π/4 and radius 12 feet? 2 What is the area of a sector of a circle with central angle by 60 and radius 2 meters? Plane Trigonometry (MTH 133) Plane Trigonometry Notes Fall / 20 Plane Trigonometry (MTH 133) Plane Trigonometry Notes Fall / 20
7 Arc Length and Sector Area Problems 1 Salem, Oregon lies approximately on the 45th parallel. If the radius of the earth is 3950 miles, how far is Salem from the North Pole? 2 A central-pivot irrigation system is watering a circular field of radius 150 feet. The system rotates π/6 radians in one hour. What is the area that is watered in one hour? 3 A bicycle has a chain that connects a chainring of radius 6 inches to a cog of radius 2 inches. If the chainring rotates through an angle of of 20, then how many degrees does the cog rotate? Plane Trigonometry (MTH 133) Plane Trigonometry Notes Fall / 20 Plane Trigonometry (MTH 133) Plane Trigonometry Notes Fall / 20
8 Angular Velocity Definition If a point is in motion on a circle through and angle of α radians in time t, then its angular velocity ω is given by ω = α t. Plane Trigonometry (MTH 133) Plane Trigonometry Notes Fall / 20 Plane Trigonometry (MTH 133) Plane Trigonometry Notes Fall / 20
9 Linear Velocity Definition If a point is in motion on a circle through and angle of α radians in time t, then its linear velocity ω is given by v = s t, where s is the arc length determined by s = αr. Fact If v is the linear velocity of a point on a circle of radius r, and ω is its angula velocity, then v = rω. Plane Trigonometry (MTH 133) Plane Trigonometry Notes Fall / 20 Plane Trigonometry (MTH 133) Plane Trigonometry Notes Fall / 20
10 Angular and Linear Velocity Problems Suppose that a vinyl record is 6.5 inches in diameter and rotates at 45 revolutions per minute. What is its angular velocity and the linear velocity of a point on the edge of the record? The radius of the earth is approximately 3950 miles. If you are standing on the equator, what is your angular velocity? What is your linear velocity? The blade on a table saw rotates at 3450 revolutions per minute. How much faster (in ft/sec) does a 12-in diameter blade strike a piece of wood than a 10 in diameter blade? Plane Trigonometry (MTH 133) Plane Trigonometry Notes Fall / 20 Plane Trigonometry (MTH 133) Plane Trigonometry Notes Fall / 20
DMS, LINEAR AND ANGULAR SPEED
DMS, LINEAR AND ANGULAR SPEED Section 4.1A Precalculus PreAP/Dual, Revised 2017 viet.dang@humbleisd.net 8/1/2018 12:13 AM 4.1B: DMS, Linear and Angular Speed 1 DEGREES MINUTES SECONDS (DMS) A. Written
Central Angles and Arcs
Advance Algebra & Trigonometry Angles & Circular Functions Central Angles and Arcs Arc Length 1. A central angle an angle whose vertex lies at the center of the circle: A B ABC is a central angle C 2.
An angle on the coordinate plane is in standard form when the vertex is on the origin and one ray lies on the positive x-axis.
Name: Topic: Main Ideas/Questions Notes/Eamples Date: Class: Angles in Standard Form y θ An angle on the coordinate plane is in standard form when the verte is on the origin and one ray lies on the positive
An can be formed by rotating one ray away from a fixed ray indicated by an arrow. The fixed. ray is the and the rotated ray is the.
Date: 1/29/19 61 Section: Objective: angle angles t their measures An can be formed by rotating one ray away from a fixed ray indicated by an arrow The fixed initial side terminal side ray is the and the
Mth 133 Trigonometry Review Problems for the Final Examination
Mth 1 Trigonometry Review Problems for the Final Examination Thomas W. Judson Stephen F. Austin State University Fall 017 Final Exam Details The final exam for MTH 1 will is comprehensive and will cover
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Arc Length, Area of Sector of a Circle, Angular and Linear Velocity Worksheet Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem.
CHAPTER 4 Trigonometry
CHAPTER Trigonometr Section. Radian and Degree Measure You should know the following basic facts about angles, their measurement, and their applications. Tpes of Angles: (a) Acute: Measure between 0 and
Precalculus Lesson 6.1: Angles and Their Measure Lesson 6.2: A Unit Circle Approach Part 2
Precalculus Lesson 6.1: Angles and Their Measure Lesson 6.2: A Unit Circle Approach Part 2 Lesson 6.2 Before we look at the unit circle with respect to the trigonometric functions, we need to get some
5.1 Angles and Their Measurements
Graduate T.A. Department of Mathematics Dnamical Sstems and Chaos San Diego State Universit November 8, 2011 A ra is the set of points which are part of a line which is finite in one direction, but infinite
Section 4.2: Radians, Arc Length, and the Area of a Sector
CHAPTER 4 Trigonometric Functions Section 4.: Radians, Arc Length, and the Area of a Sector Measure of an Angle Formulas for Arc Length and Sector Area Measure of an Angle Degree Measure: 368 SECTION 4.
Precalculus Lesson 6.1: Angles and Their Measure Mrs. Snow, Instructor
Precalculus Lesson 6.1: Angles and Their Measure Mrs. Snow, Instructor In Trigonometry we will be working with angles from We will also work with degrees that are smaller than Check out Shaun White s YouTube
150 Lecture Notes - Section 6.1 Angle Measure
c Marcia Drost, February, 008 Definition of Terms 50 Lecture Notes - Section 6. Angle Measure ray a line angle vertex two rays with a common endpoint the common endpoint initial side terminal side Standard
Example 1 Give the degree measure of the angle shown on the circle.
Section 5. Angles 307 Section 5. Angles Because many applications involving circles also involve q rotation of the circle, it is natural to introduce a measure for the rotation, or angle, between two rays
Chapter 6. Trigonometric Functions of Angles. 6.1 Angle Measure. 1 radians = 180º. π 1. To convert degrees to radians, multiply by.
Chapter 6. Trigonometric Functions of Angles 6.1 Angle Measure Radian Measure 1 radians = 180º Therefore, o 180 π 1 rad =, or π 1º = 180 rad Angle Measure Conversions π 1. To convert degrees to radians,
Chapter 5 Introduction to Trigonometric Functions
Chapter 5 Introduction to Trigonometric Functions 5.1 Angles Section Exercises Verbal 1. Draw an angle in standard position. Label the vertex, initial side, and terminal side. 2. Explain why there are
Given one trigonometric ratio and quadrant, determining the remaining function values
MATH 2412 Precalculus Sections 4.1-4.5 Trigonometry (quick review) Below is a list of topics you should be familiar with if you have completed a course recently in Trigonometry. I am going to assume knowledge
Trigonometry Final Exam Review
Name Period Trigonometry Final Exam Review 2014-2015 CHAPTER 2 RIGHT TRIANGLES 8 1. Given sin θ = and θ terminates in quadrant III, find the following: 17 a) cos θ b) tan θ c) sec θ d) csc θ 2. Use a calculator
Honors Accelerated Pre-Calculus Midterm Exam Review Name: January 2010 Chapter 1: Functions and Their Graphs
Honors Accelerated Pre-Calculus Midterm Eam Review Name: January 010 Chapter 1: Functions and Their Graphs 1. Evaluate the function at each specified value of the independent variable and simplify. 1 f
Section 5.1 Exercises
Section 5.1 Circles 79 Section 5.1 Exercises 1. Find the distance between the points (5,) and (-1,-5). Find the distance between the points (,) and (-,-). Write the equation of the circle centered at (8,
Pre-Calculus Section 8.1: Angles, Arcs, & Their Measures (including Linear & Angular Speed) 1. The graph of a function is given as follows:
Pre-Calculus Section 8.1: Angles, Arcs, & Their Measures (including Linear & Angular Speed) 1. The graph of a function is given as follows: 4. Example 1 (A): Convert each degree measure to radians: A:
Chapter 3. Radian Measure and Dynamic Trigonometry
Chapter 3 Radian Measure and Dynamic Trigonometry 1 Chapter 3 Topics Angle Measure in Radians Length, Velocity and Area of a Circular sector Unit Circle Trig and Real Numbers 2 Chapter 3.1 Angle Measure
Prof. Israel Nwaguru PLANE TRIGONOMETRY - MATH 1316, CHAPTER REVIEW
Prof. Israel Nwaguru PLANE TRIGONOMETRY - MATH 1316, CHAPTER 1.1-1.4 REVIEW Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Determine the quadrant in which
MTH 133: Plane Trigonometry
MTH 133: Plane Trigonometry The Trigonometric Functions Right Angle Trigonometry Thomas W. Judson Department of Mathematics & Statistics Stephen F. Austin State University Fall 2017 Plane Trigonometry
1.1 Angles and Degree Measure
J. Jenkins - Math 060 Notes. Angles and Degree Measure An angle is often thought of as being formed b rotating one ra awa from a fied ra indicated b an arrow. The fied ra is the initial side and the rotated
Chapter 6. Trigonometric Functions of Angles. 6.1 Angle Measure. 1 radians = 180º. π 1. To convert degrees to radians, multiply by.
Chapter 6. Trigonometric Functions of Angles 6.1 Angle Measure Radian Measure 1 radians 180º Therefore, o 180 π 1 rad, or π 1º 180 rad Angle Measure Conversions π 1. To convert degrees to radians, multiply
Chapter 3. Radian Measure and Circular Functions. Copyright 2005 Pearson Education, Inc.
Chapter 3 Radian Measure and Circular Functions Copyright 2005 Pearson Education, Inc. 3.1 Radian Measure Copyright 2005 Pearson Education, Inc. Measuring Angles Thus far we have measured angles in degrees
1. Evaluate the function at each specified value of the independent variable and simplify. f 2a.)
Honors Pre-Calculus Midterm Eam Review Name: January 04 Chapter : Functions and Their Graphs. Evaluate the function at each specified value of the independent variable and simplify. f ( ) f () b. f ( )
Important variables for problems in which an object is moving along a circular arc
Unit - Radian and Degree Measure Classwork Definitions to know: Trigonometry triangle measurement Initial side, terminal side - starting and ending Position of the ray Standard position origin if the vertex,
Section 6.1 Angles and Radian Measure Review If you measured the distance around a circle in terms of its radius, what is the unit of measure?
Section 6.1 Angles and Radian Measure Review If you measured the distance around a circle in terms of its radius, what is the unit of measure? In relationship to a circle, if I go half way around the edge
7.1 Describing Circular and Rotational Motion.notebook November 03, 2017
Describing Circular and Rotational Motion Rotational motion is the motion of objects that spin about an axis. Section 7.1 Describing Circular and Rotational Motion We use the angle θ from the positive
8.2. Areas of Circles and Sectors For use with Exploration 8.2. Essential Question How can you find the area of a sector of a circle?
8.2 Areas of Circles and Sectors For use with Exploration 8.2 Essential Question How can ou find the area of a sector of a circle? 1 EXPLORATION: Finding the Area of a Sector of a Circle Work with a partner.
G.C.B.5: Arc Length 1
Regents Exam Questions G.C.B.5: Arc Length 1 www.jmap.org Name: G.C.B.5: Arc Length 1 1 A sprinkler system is set up to water the sector shown in the accompanying diagram, with angle ABC measuring 1 radian
5.1 Arc length, area sector, vocab, coterminal, reference angles_jb A Block.notebook May 14, 2014
Objectives: Generate vocabulary flashcards for new terms. Derive formulas for arc length and area of a circular sector. Solve application problems using the arc length and area of circular sector formulas.
Chapter 5.1 Variation Direct Variation, Inverse Variation and Joint Variation
1 Chapter 5.1 Variation Direct Variation, Inverse Variation and Joint Variation Sometimes the equation that relates two or more variables can be described in words by the idea of variation. There are three
If x = 180 then the arc subtended by x is a semicircle which we know has length πr. Now we argue that:
Arclength Consider a circle of radius r and an angle of x degrees as shown in the figure below. The segment of the circle opposite the angle x is called the arc subtended by x. We need a formula for its
Unit 6 Introduction to Trigonometry Degrees and Radians (Unit 6.2)
Unit 6 Introduction to Trigonometr Degrees and Radians (Unit 6.2) William (Bill) Finch Mathematics Department Denton High School Lesson Goals When ou have completed this lesson ou will: Understand an angle
MTH 122: Section 204. Plane Trigonometry. Test 1
MTH 122: Section 204. Plane Trigonometry. Test 1 Section A: No use of calculator is allowed. Show your work and clearly identify your answer. 1. a). Complete the following table. α 0 π/6 π/4 π/3 π/2 π
Honors Pre-calculus Midterm Review
Honors Pre-calculus Midterm Review Name: Chapter 1: Functions and Their Graphs 1. Evaluate the function f(x) = x 2 + 1 at each specified value of the independent variable and simplify. a. f( 3) b. f(x
Math 1303 Part II. The opening of one of 360 equal central angles of a circle is what we chose to represent 1 degree
Math 1303 Part II We have discussed two ways of measuring angles; degrees and radians The opening of one of 360 equal central angles of a circle is what we chose to represent 1 degree We defined a radian
1. Use a calculator to find to the nearest tenth of a degree, if 0 < < 360 and
Practice Test 2 Numeric Response 1. Use a calculator to find to the nearest tenth of a degree, if 0 < < 360 and with in QIII 2. Use a calculator to find to the nearest tenth of a degree, if 0 < < 360 and
Basics of rotational motion
Basics of rotational motion Motion of bodies rotating about a given axis, like wheels, blades of a fan and a chair cannot be analyzed by treating them as a point mass or particle. At a given instant of
Enhanced Instructional Transition Guide
2012-2013 Enhanced Instructional Transition Guide High School Courses Unit Number: 03 /Mathematics Suggested Duration: 4 days Unit 03: Introduction to Trigonometry (15 days) Possible Lesson 01 (6 days)
Section 6.1. Standard position- the vertex of the ray is at the origin and the initial side lies along the positive x-axis.
1 Section 6.1 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
We define angular displacement, θ, and angular velocity, ω. What's a radian?
We define angular displacement, θ, and angular velocity, ω Units: θ = rad ω = rad/s What's a radian? Radian is the ratio between the length of an arc and its radius note: counterclockwise is + clockwise
Practice Test - Chapter 4
Find the value of x. Round to the nearest tenth, if necessary. 1. An acute angle measure and the length of the hypotenuse are given, so the sine function can be used to find the length of the side opposite.
Section 3.2 Applications of Radian Measure
Section. Applications of Radian Measure 07 (continued) 88. 80 radians = = 0 5 5 80 radians = = 00 7 5 = 5 radian s 0 = 0 radian s = radian 80 89. (a) In hours, the hour hand will rotate twice around the
IUPUI Department of Mathematical Sciences Departmental Final Examination PRACTICE FINAL EXAM VERSION #2 MATH Trigonometry
IUPUI Department of Mathematical Sciences Departmental Final Examination PRACTICE FINAL EXAM VERSION # MATH 15400 Trigonometry Exam directions similar to those on the departmental final. 1. DO NOT OPEN
We can use the Pythagorean Theorem to find the distance between two points on a graph.
Chapter 5: Trigonometric Functions of Angles In the previous chapters, we have explored a variety of functions which could be combined to form a variety of shapes. In this discussion, one common shape
Chapter 9 [ Edit ] Ladybugs on a Rotating Disk. v = ωr, where r is the distance between the object and the axis of rotation. Chapter 9. Part A.
![Chapter 9 [ Edit ] Ladybugs on a Rotating Disk. v = ωr, where r is the distance between the object and the axis of rotation. Chapter 9. Part A.](/thumbs/77/75060038.jpg "Chapter 9 [ Edit ] Ladybugs on a Rotating Disk. v = ωr, where r is the distance between the object and the axis of rotation. Chapter 9. Part A.")
Chapter 9 [ Edit ] Chapter 9 Overview Summary View Diagnostics View Print View with Answers Due: 11:59pm on Sunday, October 30, 2016 To understand how points are awarded, read the Grading Policy for this
- 5π 2. a. a. b. b. In 5 7, convert to a radian measure without using a calculator
4-1 Skills Objective A In 1 and, the measure of a rotation is given. a. Convert the measure to revolutions. b. On the circle draw a central angle showing the given rotation. 1. 5. radians - a. a. b. b.
5.1 Arc length, area sector, vocab, coterminal, reference angles_jb-a Block.notebook April 03, 2014
Objectives: Generate vocabulary flashcards for new terms. Derive formulas for arc length and area of a circular sector. Solve application problems using the arc length and area of circular sector formulas.
1.1 Find the measures of two angles, one positive and one negative, that are coterminal with the given angle. 1) 162
Math 00 Midterm Review Dugopolski Trigonometr Edition, Chapter and. Find the measures of two angles, one positive and one negative, that are coterminal with the given angle. ) ) - ) For the given angle,
4-2 Degrees and Radians
Write each decimal degree measure in DMS form and each DMS measure in decimal degree form to the nearest thousandth. 1. 11.773 First, convert 0. 773 into minutes and seconds. Next, convert 0.38' into seconds.
G.C.B.5: Arc Length 1
Regents Exam Questions G.C.B.5: Arc Length 1 www.jmap.org Name: G.C.B.5: Arc Length 1 1 A sprinkler system is set up to water the sector shown in the accompanying diagram, with angle ABC measuring 1 radian
A Short Course in Basic Trigonometry. Marcel B. Finan Arkansas Tech University c All Rights Reserved
A Short Course in Basic Trigonometry Marcel B. Finan Arkansas Tech University c All Rights Reserved PREFACE Trigonometry in modern time is an indispensable tool in Physics, engineering, computer science,
WebAssign Assignment #2: Chapter 2.1 (Homework)
WebAssign Assignment #2: Chapter 2.1 (Homework) Current Score : / 45 Due : hursday, October 8 2015 11:59 PM PD Jonah Ostroff Math124A15, section, all 2015 Instructor: Jonah Ostroff 1. /10 pointsscalce7
AFM Midterm Review I Fall Determine if the relation is a function. 1,6, 2. Determine the domain of the function. . x x
AFM Midterm Review I Fall 06. Determine if the relation is a function.,6,,, 5,. Determine the domain of the function 7 h ( ). 4. Sketch the graph of f 4. Sketch the graph of f 5. Sketch the graph of f
Rotational Kinematics, Physics. Worksheet 1: Practice working with rotation and revolution
Rotational Kinematics, Physics Worksheet 1: Practice working with rotation and revolution Circular motion can involve rotation and/or revolution. Rotation occurs when the object spins about an internal
n power Name: NOTES 2.5, Date: Period: Mrs. Nguyen s Initial: LESSON 2.5 MODELING VARIATION
NOTES 2.5, 6.1 6.3 Name: Date: Period: Mrs. Nguyen s Initial: LESSON 2.5 MODELING VARIATION Direct Variation y mx b when b 0 or y mx or y kx y kx and k 0 - y varies directly as x - y is directly proportional
16.2 Arc Length and Radian Measure
Name Class Date 16.2 rc Length and Radian Measure Essential Question: How do you find the length of an arc? Explore Deriving the Formula for rc Length n arc is an unbroken part of a circle consisting of
G.C.B.5: Arc Length 1
Regents Exam Questions G.C.B.5: Arc Length www.jmap.org Name: G.C.B.5: Arc Length The diagram below shows circle O with radii OA and OB. The measure of angle AOB is 0, and the length of a radius is inches.
Optimal Cone. 1 Grade Levels and Time. 2 Objectives and Topics. 3 Introduction. 4 Procedure and Discussion. Grades:11-12
1 Grade Levels and Time Optimal Cone Grades:11-12 Time: This lesson will take two 50-minute class periods. 2 Objectives and Topics Objectives: Topics: The students should be able to formulate the volume
11.3 areas of circles and sectors 2016 ink.notebook. April 12, Page 134 Page Areas of Circles and Sectors. Standards.
11.3 areas of circles and sectors 2016 ink.notebook Page 134 Page 133 11.3 Areas of Circles and Sectors Round to the nearest Lesson Objectives Standards Lesson Notes 11.3 Areas of Circles and Sectors Lesson
Chapter 1: Trigonometric Functions 1. Find (a) the complement and (b) the supplement of 61. Show all work and / or support your answer.
Trig Exam Review F07 O Brien Trigonometry Exam Review: Chapters,, To adequately prepare for the exam, try to work these review problems using only the trigonometry knowledge which you have internalized
Rigid Object. Chapter 10. Angular Position. Angular Position. A rigid object is one that is nondeformable
Rigid Object Chapter 10 Rotation of a Rigid Object about a Fixed Axis A rigid object is one that is nondeformable The relative locations of all particles making up the object remain constant All real objects
Trigonometric Functions. Copyright Cengage Learning. All rights reserved.
4 Trigonometric Functions Copyright Cengage Learning. All rights reserved. 4.1 Radian and Degree Measure Copyright Cengage Learning. All rights reserved. What You Should Learn Describe angles. Use radian
Radian measure and trigonometric functions on the reals
Trigonometry Radian measure and trigonometric functions on the reals The units for measuring angles tend to change depending on the context - in a geometry course, you re more likely to be measuring your
Chapter 3. Radian Measure and Circular Functions. Section 3.1: Radian Measure. π 1.57, 1 is the only integer value in the
Chapter Radian Measure and Circular Functions Section.: Radian Measure. Since θ is in quadrant I, 0 < θ
ROTATIONAL KINEMATICS
CHAPTER 8 ROTATIONAL KINEMATICS CONCEPTUAL QUESTIONS 1. REASONING AND SOLUTION The figures below show two axes in the plane of the paper and located so that the points B and C move in circular paths having
CHAPTER 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
Casting Physics Simplified Part Two. Frames of Reference
Casting Physics Simplified Part Two Part one of this paper discussed physics that applies to linear motion, i.e., motion in a straight line. This section of the paper will expand these concepts to angular
5.1: 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
5 TRIGONOMETRIC FUNCTIONS
Chapter 5 Trigonometric Functions 705 5 TRIGONOMETRIC FUNCTIONS Figure 5.1 The tide rises and falls at regular, predictable intervals. (credit: Andrea Schaffer, Flickr) 5.1 Angles 5.2 Unit Circle: Sine
Regents Exam Questions by Topic Page 1 ANGLES: Arc Length NAME:
Regents Exam Questions by Topic Page 1 1. 010725b As shown in the accompanying diagram, a dial in the shape of a semicircle has a radius of 4 centimeters. Find the measure of, in radians, when the pointer
Name Date Period. Multiple Choice
Name Date Period Worksheet 3.8 Related Rates Show all work. Calculator permitted. Show all set-ups and analysis. Report all answers to 3 decimals and avoid intermediate rounding error. Multiple Choice
2/27/2018. Relative Motion. Reference Frames. Reference Frames
Relative Motion The figure below shows Amy and Bill watching Carlos on his bicycle. According to Amy, Carlos s velocity is (v x ) CA 5 m/s. The CA subscript means C relative to A. According to Bill, Carlos
( 3 ) = (r) cos (390 ) =
MATH 7A Test 4 SAMPLE This test is in two parts. On part one, you may not use a calculator; on part two, a (non-graphing) calculator is necessary. When you complete part one, you turn it in and get part
Chapter 4 Trigonometric Functions
Chapter 4 Trigonometric Functions Overview: 4.1 Radian and Degree Measure 4.2 Trigonometric Functions: The Unit Circle 4.3 Right Triangle Trigonometry 4.4 Trigonometric Functions of Any Angle 4.5 Graphs
3x 2 + 3y 2 +18x + 6y 60 = 0. 1) C(3,1), r = 30
1. Find the center and radius of the circle with the following equation: x 2 + y 2 +18x + 6y 60 = 0. 1) C(,1), r = 0 2) C(,1), r = 0 ) C(, 1), r = 0 4) C(, 1), r = 0 5) C(9,), r = 110 6) C(9,), r =110
Fundamentals of Mathematics (MATH 1510)
Fundamentals of Mathematics () Instructor: Email: shenlili@yorku.ca Department of Mathematics and Statistics York University March 14-18, 2016 Outline 1 2 s An angle AOB consists of two rays R 1 and R
(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
College 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
GISC3325 Class 2 - Latitude and Longitude on Sphere. 28 January 2013
GISC3325 Class 2 - Latitude and Longitude on Sphere 28 January 2013 Geodesy Defined The science describing the size, shape and gravity field of the Earth in its threedimensional time-varying states. Branch
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. Use the appropriate identity to find the indicated function value. Rationalize the denominator,
Homework 3. (33-40) The graph of an exponential function is given. Match each graph to one of the following functions.
Homework Section 4. (-40) The graph of an exponential function is given. Match each graph to one of the following functions. (a)y = x (b)y = x (c)y = x (d)y = x (e)y = x (f)y = x (g)y = x (h)y = x (46,
BRONX COMMUNITY COLLEGE of the City University of New York DEPARTMENT OF MATHEMATICS & COMPUTER SCIENCE. MTH06 Review Sheet y 6 2x + 5 y.
BRONX COMMUNITY COLLEGE of the Cit Universit of New York DEPARTMENT OF MATHEMATICS & COMPUTER SCIENCE MTH06 Review Sheet. Perform the indicated operations and simplif: n n 0 n + n ( 9 )( ) + + 6 + 9ab
IB Mathematics HL Year 1 Unit 4: Trigonometry (Core Topic 3) Homework for Unit 4. (A) Using the diagram to the right show that
IB Mathematics HL Year Unit 4: Trigonometry (Core Topic 3) Homework for Unit 4 Lesson 4 Review I: radian measure, definitions of trig ratios, and areas of triangles D.2: 5; E.: 5; E.2: 4, 6; F: 3, 5, 7,
AP Physics 1 Lesson 15.a Rotational Kinematics Graphical Analysis and Kinematic Equation Use. Name. Date. Period. Engage
AP Physics 1 Lesson 15.a Rotational Kinematics Graphical Analysis and Kinematic Equation Use Name Outcomes Date Interpret graphical evidence of angular motion (uniform speed & uniform acceleration). Apply
Old Math 120 Exams. David M. McClendon. Department of Mathematics Ferris State University
Old Math 10 Exams David M. McClendon Department of Mathematics Ferris State University 1 Contents Contents Contents 1 General comments on these exams 3 Exams from Fall 016 4.1 Fall 016 Exam 1...............................
Math 30-1: Trigonometry One PRACTICE EXAM
Math 30-1: Trigonometry One PRACTICE EXAM 1. The angle 210 is equivalent to: degrees radians degrees radians 2. The reference angle of is: radians radians radians radians 3. The principal angle of 9.00
Test, Lesson 7 Waves - Answer Key Page 1
Test, Lesson 7 Waves - Answer Key Page 1 1. Match the proper units with the following: W. wavelength 1. nm F. frequency 2. /sec V. velocity 3. m 4. ms -1 5. Hz 6. m/sec (A) W: 1, 3 F: 2, 4, 5 V: 6 (B)
Math 175: Chapter 6 Review: Trigonometric Functions
Math 175: Chapter 6 Review: Trigonometric Functions In order to prepare for a test on Chapter 6, you need to understand and be able to work problems involving the following topics. A. Can you sketch an
BRONX COMMUNITY COLLEGE of the City University of New York DEPARTMENT OF MATHEMATICS & COMPUTER SCIENCE. MTH06 Review Sheet y 6 2x + 5 y.
BRONX COMMUNITY COLLEGE of the Cit Universit of New York DEPARTMENT OF MATHEMATICS & COMPUTER SCIENCE MTH06 Review Sheet. Perform the indicated operations and simplif: n n 0 n + n ( 9 ) ( ) + + 6 + 9ab
Mth 076: Applied Geometry (Individualized Sections) MODULE FOUR STUDY GUIDE
Mth 076: pplied Geometry (Individualized Sections) MODULE FOUR STUDY GUIDE INTRODUTION TO GEOMETRY Pick up Geometric Formula Sheet (This sheet may be used while testing) ssignment Eleven: Problems Involving
1. Which of the following is the unit for angular displacement? A. Meters B. Seconds C. Radians D. Radian per second E. Inches
AP Physics B Practice Questions: Rotational Motion Multiple-Choice Questions 1. Which of the following is the unit for angular displacement? A. Meters B. Seconds C. Radians D. Radian per second E. Inches
1.1 Angles, Degrees, and Arcs
MA140 Trig 2015 Homework p. 1 Name: 1.1 Angles, Degrees, and Arcs Find the fraction of a counterclockwise revolution that will form an angle with the indicated number of degrees. 3(a). 45 3(b). 150 3(c).
11.2 Start Thinking Warm Up Cumulative Review Warm Up
11.2 Start Thinking The circle in the diagram has a diameter of 14 inches. What is the area of the circle? Use the area of the circle to calculate the area of the sector created b the given measure of
UNC Charlotte 2010 Algebra with solutions March 8, 2010
with solutions March 8, 2010 1. Let y = mx + b be the image when the line x 3y + 11 = 0 is reflected across the x-axis. The value of m + b is: (A) 6 (B) 5 (C) 4 (D) 3 (E) 2 Solution: C. The slope of the
MCPS Algebra 2 and Precalculus Standards, Categories, and Indicators*
Content Standard 1.0 (HS) Patterns, Algebra and Functions Students will algebraically represent, model, analyze, and solve mathematical and real-world problems involving functional patterns and relationships.
8, x 2. 4and. 4, y 1. y 2. x 1. Name. Part 1: (Skills) Each question is worth 2 points. SHOW ALL WORK IN THE SPACE PROVIDED. 1.
MATH 099 PRACTICE FINAL EXAMINATION Fall 2016 Name Part 1: (Skills) Each question is worth 2 points. SHOW ALL WORK IN THE SPACE PROVIDED. 1. Determine whether 4, 3 is a solution to the equation 3x 3y 21