2.5 Using the Sine and Cosine Ratios to Calculate Lengths
|
|
|
- Clifton McCoy
- 6 years ago
- Views:
Transcription
1 2.5 Using the ine and Cosine atios to Calculate Lengths FOCU Use the sine and cosine ratios to determine lengths. To use the sine or cosine ratio to find the length of a leg, we need to know: the measure of an acute angle, and the length of the Example 1 Using the ine or Cosine atio to Find the Length of a Leg Find the length of to the nearest tenth of a metre m olution The measure of is known. is the side adjacent to. is the. o, use the cosine ratio. cos side adjacent to adjacent to m cos ubstitute: 28 and 9.6 cos 28 Multiply both sides by cos cos 28 Use a calculator is about 8.5 m long Copyright 2011 Pearson Canada Inc. 97
2 Check 1. Find the length of each indicated side to the nearest tenth of a centimetre. a) AC B cm The measure of B is known. AC is the. BC is the. o, use the ratio. side B A C B BC AC AC is about long. b) DE E F The measure of is known. DE is the. DF is the. o, use the ratio. D cm DE is about long Copyright 2011 Pearson Canada Inc.
3 To use the sine or cosine ratio to find the length of the, we need to know: the measure of an acute angle, and the length of one leg Example 2 Using the ine or Cosine atio to Find the Length of the Hypotenuse Find the length of the to the nearest tenth of a centimetre. N 9.5 cm The is the side opposite the right angle. M 52 P olution The measure of M is known. NP is the side opposite M. MN is the. o, use the sine ratio to write an equation. sin M NP sin M ubstitute: M 52 and NP 9.5 MN 9.5 sin 52 MN Multiply both sides by MN. MN sin Divide both sides by sin 52. MN sin 52 sin 52 side opposite M 9.5 sin 52 M 52 N opposite M 9.5 cm P MN 9.5 sin 52 MN MN is about 12.1 cm long. Use a calculator Copyright 2011 Pearson Canada Inc. 99
4 Check 1. Find the length of each to the nearest tenth of a centimetre. a) K 17.4 cm side sin J M sin J 39 J The measure of J is known. The side opposite J is: The is: Use the sine ratio. sin sin JK JK JK is about long. b) cm is the side. is the. o, use the ratio. is about long Copyright 2011 Pearson Canada Inc.
5 Example 3 Using ine or Cosine to olve a Problem A surveyor makes the measurements shown in the diagram to find the distance between two observation towers on opposite sides of a river. How far apart are the towers? Give the answer to the nearest metre. iver Tower m Tower 2 olution The distance between the towers is the, AC. A Tower 1 B 63 m 73 C Tower 2 The measure of C is known. BC is the side adjacent to C. AC is the. o, use the cosine ratio. side adjacent to C cos C BC cos C ubstitute: C 73 and BC 63 AC 63 cos 73 AC Multiply both sides by AC. AC cos Divide both sides by cos AC cos 73 Use a calculator. AC The distance between the towers is about 215 m Copyright 2011 Pearson Canada Inc. 101
6 Check 1. am and ofia are building a wooden ramp for skateboarding. The height of the ramp is 0.75 m. The ramp makes an angle of 8 with the ground. What length of plywood do am and ofia need for the top of the ramp? Give your answer to the nearest tenth of a metre. E D 8 We want to find the length of DE. The measure of D is known. The side opposite D is: The is: o, use the sine ratio. F 0.75 m sin D opposite sin D ubstitute: sin sin Multiply both sides by. Divide both sides by. DE am and ofia need about of plywood. Practice 1. Which ratio would you use to find each length? a) XY b) T X T Z 29 Y 17.6 cm YZ is the side. XY is the. o, use the ratio. 53 U 15.9 cm T is the side. U is the. o, use the ratio Copyright 2011 Pearson Canada Inc.
7 2. Find the length of each indicated side to the nearest tenth of a centimetre. a) VW U V cm W The measure of is known. The side opposite is. The is. o, use the ratio. side sin sin sin sin VW VW is about long. b) 10.5 cm 36 is the. is the. o, use the ratio. is about long Copyright 2011 Pearson Canada Inc. 103
8 3. Find the length of side PM to the nearest tenth of a metre. P M The measure of is known. N 16.0 m 19 PM is the side. MN is the. o, use the ratio. PM is about long. 4. Find the length of each to the nearest tenth of a centimetre. a) E b) X 29 W cm Y G 8.4 cm F The side opposite is: The is: o, use the sine ratio. WY is the side. WX is the. o, use the ratio. sin opposite sin sin WX WX is about long. sin EF EF EF is about long Copyright 2011 Pearson Canada Inc.
9 5. A straight slide in a playground makes an angle of 28 with the ground. The slide covers a horizontal distance of 4.5 m. How long is the slide? Give your answer to the nearest tenth of a metre. The measure of is known. The side adjacent to is: The is: o, use the ratio m The slide is about long. 6. A 15-m support cable joins the top of a telephone pole to a point on the ground. The cable makes an angle of 32 with the ground. Find the height of the pole to the nearest tenth of a metre. C E 15.0 m 32 D The height of the pole is about Copyright 2011 Pearson Canada Inc. 105
Chapter 8 Practice Test
Chapter 8 Practice Test Multiple Choice Identify the choice that best completes the statement or answers the question. 1. In triangle ABC, is a right angle and 45. Find BC. If you answer is not an integer,
Chapter 11 Trigonometric Ratios The Sine Ratio
Chapter 11 Trigonometric Ratios 11.2 The Sine Ratio Introduction The figure below shows a right-angled triangle ABC, where B = and C = 90. A hypotenuse B θ adjacent side of opposite side of C AB is called
13.2 Define General Angles and Use Radian Measure. standard position:
3.2 Define General Angles and Use Radian Measure standard position: Examples: Draw an angle with the given measure in standard position..) 240 o 2.) 500 o 3.) -50 o Apr 7 9:55 AM coterminal angles: Examples:
Using Trigonometric Ratios Part 1: Solving For Unknown Sides
MPM2D: Principles of Mathematics Using Trigonometric Ratios Part 1: Solving For Unknown Sides J. Garvin Slide 1/15 Recap State the three primary trigonometric ratios for A in ABC. Slide 2/15 Recap State
How to work out trig functions of angles without a scientific calculator
Before starting, you will need to understand how to use SOH CAH TOA. How to work out trig functions of angles without a scientific calculator Task 1 sine and cosine Work out sin 23 and cos 23 by constructing
13.4 Chapter 13: Trigonometric Ratios and Functions. Section 13.4
13.4 Chapter 13: Trigonometric Ratios and Functions Section 13.4 1 13.4 Chapter 13: Trigonometric Ratios and Functions Section 13.4 2 Key Concept Section 13.4 3 Key Concept Section 13.4 4 Key Concept Section
MHR Foundations for College Mathematics 11 Solutions 1. Chapter 1 Prerequisite Skills. Chapter 1 Prerequisite Skills Question 1 Page 4 = 6+ =
Chapter 1 Trigonometry Chapter 1 Prerequisite Skills Chapter 1 Prerequisite Skills Question 1 Page 4 a) x 36 b) x 6 19 x ± 36 x ± 6 x x 6+ 19 5 x ± 5 x ± 5 c) x 64 + 36 d) x 5 + 1 x 100 x 5 + 144 x ± 100
3-5 Slopes of Lines. Warm Up Lesson Presentation Lesson Quiz. Holt McDougal Geometry
3-5 Slopes of Lines Warm Up Lesson Presentation Lesson Quiz Geometry Warm Up Find the value of m. 1. 2. 3. 4. undefined 0 Objectives Find the slope of a line. Use slopes to identify parallel and perpendicular
CC Geometry H Aim #3: How do we rotate points 90 degrees on the coordinate plane? Do Now:
CC Geometry H Aim #3: How do we rotate points 90 degrees on the coordinate plane? Do Now: 1. a. Write the equation of the line that has a slope of m = and passes through the point (0, 3). Graph this equation
8-1 Similarity in Right Triangles
8-1 Similarity in Right Triangles In this chapter about right triangles, you will be working with radicals, such as 19 and 2 5. radical is in simplest form when: 1. No perfect square factor other then
GAP CLOSING. Powers and Roots. Intermediate / Senior Student Book GAP CLOSING. Powers and Roots. Intermediate / Senior Student Book
GAP CLOSING Powers and Roots GAP CLOSING Powers and Roots Intermediate / Senior Student Book Intermediate / Senior Student Book Powers and Roots Diagnostic...3 Perfect Squares and Square Roots...6 Powers...
Representing Square Numbers. Use materials to represent square numbers. A. Calculate the number of counters in this square array.
1.1 Student book page 4 Representing Square Numbers You will need counters a calculator Use materials to represent square numbers. A. Calculate the number of counters in this square array. 5 5 25 number
May 03, AdvAlg10 3PropertiesOfTrigonometricRatios.notebook. a. sin17 o b. cos 73 o c. sin 65 o d. cos 25 o. sin(a) = cos (90 A) Mar 9 10:08 PM
a. sin17 o b. cos 73 o c. sin 65 o d. cos 25 o sin(a) = cos (90 A) Mar 9 10:08 PM 1 Find another pair of angle measures x and y that illustrates the pattern cos x = sin y. Mar 9 10:11 PM 2 If two angles
March 29, AdvAlg10 3PropertiesOfTrigonometricRatios.notebook. a. sin17 o b. cos 73 o c. sin 65 o d. cos 25 o. sin(a) = cos (90 A) Mar 9 10:08 PM
a. sin17 o b. cos 73 o c. sin 65 o d. cos 25 o sin(a) = cos (90 A) Mar 9 10:08 PM 1 Find another pair of angle measures x and y that illustrates the pattern cos x = sin y. Mar 9 10:11 PM 2 If two angles
Pythagorean Theorem: Trigonometry Packet #1 S O H C A H T O A. Examples Evaluate the six trig functions of the angle θ. 1.) 2.)
Trigonometry Packet #1 opposite side hypotenuse Name: Objectives: Students will be able to solve triangles using trig ratios and find trig ratios of a given angle. S O H C A H T O A adjacent side θ Right
Similar Figures Review #2
Similar Figures Review #2 Name: Date: 1. If XYZ is similar to STU, what is the length of XY in centimeters? 3. Use the triangle below to answer the following question(s). A. 9. 10.5. 12 D. 12.5 In A above,
5.1 Graphing Sine and Cosine Functions.notebook. Chapter 5: Trigonometric Functions and Graphs
Chapter 5: Trigonometric Functions and Graphs 1 Chapter 5 5.1 Graphing Sine and Cosine Functions Pages 222 237 Complete the following table using your calculator. Round answers to the nearest tenth. 2
Section 5.1 Angles and Radian Measure. Ever Feel Like You re Just Going in Circles?
Section 5.1 Angles and Radian Measure Ever Feel Like You re Just Going in Circles? You re riding on a Ferris wheel and wonder how fast you are traveling. Before you got on the ride, the operator told you
Right Triangle Trigonometry (Section 4-3)
Right Triangle Trigonometry (Section 4-3) Essential Question: How does the Pythagorean Theorem apply to right triangle trigonometry? Students will write a summary describing the relationship between the
1. A maintenance technician sights the top of a telephone pole at a 25 angle of elevation as shown.
Name 1. A maintenance technician sights the top of a telephone pole at a 25 angle of elevation as shown. Determine the horizontal distance between the technician and the base of the telephone pole to the
Unit 5. Algebra 2. Name:
Unit 5 Algebra 2 Name: 12.1 Day 1: Trigonometric Functions in Right Triangles Vocabulary, Main Topics, and Questions Definitions, Diagrams and Examples Theta Opposite Side of an Angle Adjacent Side of
Create Your Own Triangles Learning Task
Create Your Own Triangles Learning Task Supplies needed Heavy stock, smooth unlined paper for constructing triangles (unlined index cards, white or pastel colors are a good choice) Unlined paper (if students
International mathematical olympiad Formula of Unity / The Third Millenium 2013/2014 year
1st round, grade R5 * example, all years from 1988 to 2012 were hard. Find the maximal number of consecutive hard years among the past years of Common Era (A.D.). 2. There are 6 candles on a round cake.
Date: Worksheet 4-8: Problem Solving with Trigonometry
Worksheet 4-8: Problem Solving with Trigonometry Step 1: Read the question carefully. Pay attention to special terminology. Step 2: Draw a triangle to illustrate the situation. Decide on whether the triangle
Chapter 2: Pythagoras Theorem and Trigonometry (Revision)
Chapter 2: Pythagoras Theorem and Trigonometry (Revision) Paper 1 & 2B 2A 3.1.3 Triangles Understand a proof of Pythagoras Theorem. Understand the converse of Pythagoras Theorem. Use Pythagoras 3.1.3 Triangles
Squares and Square Roots Algebra 11.1
Squares and Square Roots Algebra 11.1 To square a number, multiply the number by itself. Practice: Solve. 1. 1. 0.6. (9) 4. 10 11 Squares and Square Roots are Inverse Operations. If =y then is a square
Square Roots and the Pythagorean Theorem
UNIT 1 Square Roots and the Pythagorean Theorem Just for Fun What Do You Notice? Follow the steps. An example is given. Example 1. Pick a 4-digit number with different digits. 3078 2. Find the greatest
GEO: Sem 1 Unit 1 Review of Geometry on the Coordinate Plane Section 1.6: Midpoint and Distance in the Coordinate Plane (1)
GEO: Sem 1 Unit 1 Review of Geometr on the Coordinate Plane Section 1.6: Midpoint and Distance in the Coordinate Plane (1) NAME OJECTIVES: WARM UP Develop and appl the formula for midpoint. Use the Distance
The CENTRE for EDUCATION in MATHEMATICS and COMPUTING cemc.uwaterloo.ca Galois Contest. Thursday, April 18, 2013
The CENTRE for EDUCATION in MATHEMATIC and COMUTING cemc.uwaterloo.ca 201 Galois Contest Thursday, April 18, 201 (in North America and outh America) Friday, April 19, 201 (outside of North America and
Student Instruction Sheet: Unit 4 Lesson 1. Pythagorean Theorem
Student Instruction Sheet: Unit 4 Lesson 1 Suggested time: 75 minutes Pythagorean Theorem What s important in this lesson: In this lesson you will learn the Pythagorean Theorem and how to apply the theorem
cos sin sin 2 60 = 1.
Name: Class: Date: Use the definitions to evaluate the six trigonometric functions of. In cases in which a radical occurs in a denominator, rationalize the denominator. Suppose that ABC is a right triangle
Activity 11 OBJECTIVE. MATERIAL REQUIRED Cardboard, white paper, graph paper with various given points, geometry box, pen/pencil.
Activity 11 OBJECTIVE To find the values of abscissae and ordinates of various points given in a cartesian plane. MATERIAL REQUIRED Cardboard, white paper, graph paper with various given points, geometry
Trigonometric ratios 9B 1 a d b 2 a c b
Trigonometric ratios 9B 1 a a Using sin A sin B 8 sin 72 sin 30 8sin 72 sin 30 As 72 > 30, > 8 cm 15.2 cm ( ) ABC 180 68.4 + 83.7 27.9 Using a 9.8 sin 27.9 sin 83.7 9.8sin 27.9 a sin 83.7 4.61 cm ( ) 2
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Math 1316 Ch.1-2 Review Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 1) Find the supplement of an angle whose
Section 8.4: The Equations of Sinusoidal Functions
Section 8.4: The Equations of Sinusoidal Functions In this section, we will examine transformations of the sine and cosine function and learn how to read various properties from the equation. Transformed
1. Write the angles in order from 2. Write the side lengths in order from
Lesson 1 Assignment Triangle Inequalities 1. Write the angles in order from 2. Write the side lengths in order from smallest to largest. shortest to longest. 3. Tell whether a triangle can have the sides
In this section, you will learn the basic trigonometric identities and how to use them to prove other identities.
4.6 Trigonometric Identities Solutions to equations that arise from real-world problems sometimes include trigonometric terms. One example is a trajectory problem. If a volleyball player serves a ball
Math Problem Set 5. Name: Neal Nelson. Show Scored View #1 Points possible: 1. Total attempts: 2
Math Problem Set 5 Show Scored View #1 Points possible: 1. Total attempts: (a) The angle between 0 and 60 that is coterminal with the 69 angle is degrees. (b) The angle between 0 and 60 that is coterminal
In a right-angled triangle, the side opposite the right angle is called the hypotenuse.
MATHEMATICAL APPLICATIONS 1 WEEK 14 NOTES & EXERCISES In a right-angled triangle, the side opposite the right angle is called the hypotenuse. The other two sides are named in relation to the angle in question,
Chapter 1 and Section 2.1
Chapter 1 and Section 2.1 Diana Pell Section 1.1: Angles, Degrees, and Special Triangles Angles Degree Measure Angles that measure 90 are called right angles. Angles that measure between 0 and 90 are called
6.2 Slopes of Parallel and Perpendicular Lines
. Slopes of Parallel and Perpendicular Lines FOCUS Use slope to find out if two lines are parallel or perpendicular. These two lines are parallel. Slope of line AB Slope of line CD These two lines have
2. Here are some triangles. (a) Write down the letter of the triangle that is. right-angled, ... (ii) isosceles. ... (2)
Topic 8 Shapes 2. Here are some triangles. A B C D F E G (a) Write down the letter of the triangle that is (i) right-angled,... (ii) isosceles.... (2) Two of the triangles are congruent. (b) Write down
Trigonometry. An Overview of Important Topics
Trigonometry An Overview of Important Topics 1 Contents Trigonometry An Overview of Important Topics... 4 UNDERSTAND HOW ANGLES ARE MEASURED... 6 Degrees... 7 Radians... 7 Unit Circle... 9 Practice Problems...
MATH 130 FINAL REVIEW version2
MATH 130 FINAL REVIEW version2 Problems 1 3 refer to triangle ABC, with =. Find the remaining angle(s) and side(s). 1. =50, =25 a) =40,=32.6,=21.0 b) =50,=21.0,=32.6 c) =40,=21.0,=32.6 d) =50,=32.6,=21.0
1. 1 Square Numbers and Area Models (pp. 6-10)
Math 8 Unit 1 Notes Name: 1. 1 Square Numbers and Area Models (pp. 6-10) square number: the product of a number multiplied by itself; for example, 25 is the square of 5 perfect square: a number that is
Chapter #2 test sinusoidal function
Chapter #2 test sinusoidal function Sunday, October 07, 2012 11:23 AM Multiple Choice [ /10] Identify the choice that best completes the statement or answers the question. 1. For the function y = sin x,
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Trigonometry Final Exam Study Guide Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. The graph of a polar equation is given. Select the polar
PreCalc 11 Chapter 6 Rev Pack v1 Answer Section
PreCalc 11 Chapter 6 Rev Pack v1 Answer Section MULTIPLE CHOICE 1. ANS: A PTS: 0 DIF: Moderate 2. ANS: D PTS: 0 DIF: Easy REF: 6.1 Angles in Standard Position in Quadrant 1 LOC: 11.T1. ANS: A PTS: 0 DIF:
Practice Test (page 201) 1. A. This is not true because 64 has these factors: 1, 2, 4, 8, 16, 32, and 64 So, A is the correct answer.
Practice Test (page 201) 1. A. This is not true because 64 has these factors: 1, 2, 4, 8, 16, 32, and 64 So, A is the correct answer. 2. Expand each product until the trinomial matches the given trinomial.
3. Use your unit circle and fill in the exact values of the cosine function for each of the following angles (measured in radians).
Graphing Sine and Cosine Functions Desmos Activity 1. Use your unit circle and fill in the exact values of the sine function for each of the following angles (measured in radians). sin 0 sin π 2 sin π
1-2 Measuring and Constructing Segments. Holt Geometry
1-2 Measuring and Constructing Segments Objectives Use length and midpoint of a segment. Construct midpoints and congruent segments. Vocabulary coordinate midpoint distance bisect length segment bisector
ACCELERATED MATHEMATICS CHAPTER 14 PYTHAGOREAN THEOREM TOPICS COVERED: Simplifying Radicals Pythagorean Theorem Distance formula
ACCELERATED MATHEMATICS CHAPTER 14 PYTHAGOREAN THEOREM TOPICS COVERED: Simplifying Radicals Pythagorean Theorem Distance formula Activity 14-1: Simplifying Radicals In this chapter, radicals are going
2. Be able to evaluate a trig function at a particular degree measure. Example: cos. again, just use the unit circle!
Study Guide for PART II of the Fall 18 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 be
A. 100 B. 110 C. 115 D. 145 E. 210
Practice Quiz Polygons Area Perimeter Volume 1. Two angles of a hexagon measure 140 each. The other four angles are equal in measure. What is the measure of each of the other four equal angles, in degrees?
Name: A Trigonometric Review June 2012
Name: A Trigonometric Review June 202 This homework will prepare you for in-class work tomorrow on describing oscillations. If you need help, there are several resources: tutoring on the third floor of
Math 3 Trigonometry Part 2 Waves & Laws
Math 3 Trigonometry Part 2 Waves & Laws GRAPHING SINE AND COSINE Graph of sine function: Plotting every angle and its corresponding sine value, which is the y-coordinate, for different angles on the unit
Perpendicular and Parallel Line Segments
10 Chapter Lesson 10.1 erpendicular and arallel Line Segments Drawing erpendicular Line Segments Use a protractor to draw perpendicular line segments. 1. Draw a line segment perpendicular to Q at point.
6.1B Lesson: Building Triangles Given Three Measurements*
6.1 Lesson: uilding Triangles Given Three Measurements* Name: Period: 1. ircle all the triangles with side lengths 8 and 5 and an included angle of 32. a. b. c. 2. ircle all the triangles with side lengths
AREA See the Math Notes box in Lesson for more information about area.
AREA..1.. After measuring various angles, students look at measurement in more familiar situations, those of length and area on a flat surface. Students develop methods and formulas for calculating the
Year 10 Term 1 Homework
Yimin Math Centre Year 10 Term 1 Homework Student Name: Grade: Date: Score: Table of contents 6 Year 10 Term 1 Week 6 Homework 1 6.1 Triangle trigonometry................................... 1 6.1.1 The
Semester 1 Final Exam Review
Target 1: Vocabulary and notation Semester 1 Final Exam Review Name 1. Find the intersection of MN and LO. 2. 3) Vocabulary: Define the following terms and draw a diagram to match: a) Point b) Line c)
Mod E - Trigonometry. Wednesday, July 27, M132-Blank NotesMOM Page 1
M132-Blank NotesMOM Page 1 Mod E - Trigonometry Wednesday, July 27, 2016 12:13 PM E.0. Circles E.1. Angles E.2. Right Triangle Trigonometry E.3. Points on Circles Using Sine and Cosine E.4. The Other Trigonometric
4.2 Proving and Applying
YOU WILL NEED alulator ruler EXPLORE 4.2 Proving and Applying the Sine and Cosine Laws for Obtuse Triangles An isoseles obtuse triangle has one angle that measures 120 and one side length that is 5 m.
Trigonometry Review Tutorial Shorter Version
Author: Michael Migdail-Smith Originally developed: 007 Last updated: June 4, 0 Tutorial Shorter Version Avery Point Academic Center Trigonometric Functions The unit circle. Radians vs. Degrees Computing
Fdaytalk.com SILVER ALL. All positive. (+ve) Rest all ( -ve ) CUPS TEA. (180+θ ) & (270-
SILVER (90+θ) & (180- θ) Sinθ & cosecθ (+ve) Rest all ( -ve ) TEA (180+θ ) & (70- θ) Tanθ & Cotθ ( +ve) Rest all ( -ve ) ALL (90- θ) & (360+θ) All positive CUPS (70+θ ) & (360-θ) Cosθ & secθ ( +ve ) Rest
GAP CLOSING. Powers and Roots. Intermediate / Senior Facilitator Guide
GAP CLOSING Powers and Roots Intermediate / Senior Facilitator Guide Powers and Roots Diagnostic...5 Administer the diagnostic...5 Using diagnostic results to personalize interventions...5 Solutions...5
Trigonometry LESSON ONE - Degrees and Radians Lesson Notes
8 = 6 Trigonometry LESSON ONE - Degrees and Radians Example : Define each term or phrase and draw a sample angle. Angle in standard position. b) Positive and negative angles. Draw. c) Reference angle.
a. b. c. d. 3. Ricky jogs 5 laps around a track in 8 minutes. Which of the following would be the same number of laps per minute?
Indicate the answer choice that best completes the statement or answers the question. 1. Jake goes to the grocery store and buys 3 apples, 2 cans of soup, and 1 box of cereal. The apples cost $0.89 each;
Lesson 27: Sine and Cosine of Complementary and Special Angles
Lesson 7 M Classwork Example 1 If α and β are the measurements of complementary angles, then we are going to show that sin α = cos β. In right triangle ABC, the measurement of acute angle A is denoted
Trigonometry: A Brief Conversation
Cit Universit of New York (CUNY) CUNY Academic Works Open Educational Resources Queensborough Communit College 018 Trigonometr: A Brief Conversation Caroln D. King PhD CUNY Queensborough Communit College
Special Right Triangles and Right Triangle Trigonometry
Special Right Triangles and Right Triangle Trigonometry Reporting Category Topic Triangles Investigating special right triangles and right triangle trigonometry Primary SOL G.8 The student will solve real-world
Recording Test. Layout
Recording Test In advance of the 2012 excavation on the designated wreck site of HMS Colossus an appraisal of finds positioning methods was undertaken. In any underwater archaeological excavation, one
Foundations of Math 11: Unit 2 Proportions. The scale factor can be written as a ratio, fraction, decimal, or percentage
Lesson 2.3 Scale Name: Definitions 1) Scale: 2) Scale Factor: The scale factor can be written as a ratio, fraction, decimal, or percentage Formula: Formula: Example #1: A small electronic part measures
MATHEMATICS (UNITISED SCHEME) UNIT 1: Mathematics in Everyday Life HIGHER TIER
Surname Centre Number Candidate Number Other Names 0 GCSE 4351/02 S15-4351-02 MATHEMATICS (UNITISED SCHEME) UNIT 1: Mathematics in Everyday Life HIGHER TIER A.M. THURSDAY, 21 May 2015 1 hour 15 minutes
Geometry. Interim Test Form 3. Student Name: Teacher Name: School: Date:
Geometry Interim Test Form 3 Student Name: Teacher Name: School: Date: Mathematics Session 1: No Calculator Directions: Session 1: No Calculator Today, you will take Session 1 of the Geometry Interim
Mathematics Book 2. Grade. Name
Mathematics Grade 8 March 13 17, 2006 Name 47954 Developed and published by CTB/McGraw-Hill LLC, a subsidiary of The McGraw-Hill Companies, Inc., 20 Ryan Ranch Road, Monterey, California 93940-5703. Copyright
Getting Triggy With It
Getting Triggy With It Date: 15 May 2013 Topic: Pythagorean Theorem and Trigonometric Ratios Class: Grade 9 Ability Level: Mixed Ability Teacher: Mr. Cyrus Alvarez LESSON OBJECTIVES: At the end of the
Building Blocks of Geometry
Practice A Building Blocks of Geometry Write the following in geometric notation. 1. line EF 2. ray RS 3. line segment JK Choose the letter for the best answer. 4. Identify a line. A BD B AD C CB D BD
Unit 8 Trigonometry. Math III Mrs. Valentine
Unit 8 Trigonometry Math III Mrs. Valentine 8A.1 Angles and Periodic Data * Identifying Cycles and Periods * A periodic function is a function that repeats a pattern of y- values (outputs) at regular intervals.
Using column addition, keep the decimal points aligned one beneath the other to keep the correct place value of the digits.
Q1-5. Using column addition, keep the decimal points aligned one beneath the other to keep the correct place value of the digits. Q1. 1. 6 3 8. 2 + 3. 2 5 4 3. 0 5 [1.6 + 38.2 + 3.25 = 43.05] Q2. 0. 1
th Grade Test. A. 128 m B. 16π m C. 128π m
1. Which of the following is the greatest? A. 1 888 B. 2 777 C. 3 666 D. 4 555 E. 6 444 2. How many whole numbers between 1 and 100,000 end with the digits 123? A. 50 B. 76 C. 99 D. 100 E. 101 3. If the
6.1 - Introduction to Periodic Functions
6.1 - Introduction to Periodic Functions Periodic Functions: Period, Midline, and Amplitude In general: A function f is periodic if its values repeat at regular intervals. Graphically, this means that
^ath 9 - Chapter 1 and 4 Review
Name: Class: Date: ^ath 9 - Chapter 1 and 4 Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. What does the dashed line in the diagram represent?
Lesson: Pythagorean Theorem Lesson Topic: Use Pythagorean theorem to calculate the hypotenuse
Lesson: Pythagorean Theorem Lesson Topic: Use Pythagorean theorem to calculate the hypotenuse Question 1: What is the length of the hypotenuse? ft Question 2: What is the length of the hypotenuse? m Question
GCSE Mathematics Non Calculator Foundation Tier Mock 1, paper 1 ANSWERS 1 hour 45 minutes. Legend used in answers
MathsMadeEasy 3 GCSE Mathematics Non Calculator Foundation Tier Mock 1, paper 1 ANSWERS 1 hour 45 minutes Legend used in answers Blue dotted boxes instructions or key points Start with a column or row
Objective: Use a compass and straight edge to construct congruent segments and angles.
CONSTRUCTIONS Objective: Use a compass and straight edge to construct congruent segments and angles. Oct 1 8:33 AM Oct 2 7:42 AM 1 Introduction to Constructions Constructions: The drawing of various shapes
FOR OFFICIAL USE Total Mark
FOR OFFICIAL USE Total Mark NATIONAL QUALIFICATIONS 2014 MATHEMATICS INTERMEDIATE 1 Units 1, 2 and 3 Paper 2 TUESDAY, 6 MAY 9.55 AM 10.50 AM *X1001002* X100/10/02 Fill in these boxes and read what is printed
Double-Angle and Half-Angle Identities
7-4 OBJECTIVE Use the doubleand half-angle identities for the sine, ine, and tangent functions. Double-Angle and Half-Angle Identities ARCHITECTURE Mike MacDonald is an architect who designs water fountains.
1. Measure angle in degrees and radians 2. Find coterminal angles 3. Determine the arc length of a circle
Pre- Calculus Mathematics 12 5.1 Trigonometric Functions Goal: 1. Measure angle in degrees and radians 2. Find coterminal angles 3. Determine the arc length of a circle Measuring Angles: Angles in Standard
Lesson 1 Area of Parallelograms
NAME DATE PERIOD Lesson 1 Area of Parallelograms Words Formula The area A of a parallelogram is the product of any b and its h. Model Step 1: Write the Step 2: Replace letters with information from picture
Areas of Tropezoids, Rhombuses, and Kites
102 Areas of Tropezoids, Rhombuses, and Kites MathemaHcs Florida Standards MAFS.912.G-MG.1.1 Use geometric shapes, their measures, and their properties to describe objects. MP1. MP3, MP 4,MP6 Objective
Practice Test Chapter 8 Sinusoidal Functions
FOM 12 Practice Test Chapter 8 Sinusoidal Functions Name: Multiple Choice Identify the choice that best completes the statement or answers the question. Block: _ 1. Convert 120 into radians. A. 2 3 B.
5/6 Lesson: Angles, measurement, right triangle trig, and Pythagorean theorem
5/6 Lesson: Angles, measurement, right triangle trig, and Pythagorean theorem I. Lesson Objectives: -Students will be able to recall definitions of angles, how to measure angles, and measurement systems
Page 1 of 11 Name: 1. If tan A= 0.4548, find the measure of 1. 22 3. 24 2. 23 4. 25 A to the nearest degree. 2. The straight string of a kite makes an angle of elevation from the ground of 60. The length
Trigonometric Identities. Copyright 2017, 2013, 2009 Pearson Education, Inc.
5 Trigonometric Identities Copyright 2017, 2013, 2009 Pearson Education, Inc. 1 5.5 Double-Angle Double-Angle Identities An Application Product-to-Sum and Sum-to-Product Identities Copyright 2017, 2013,
Block D: Calculating, measuring and understanding shape Unit 1 10 days
1 of 7 The National Strategies Primary Key - Italic text signifies objectives which do not appear in the single-age version of this unit but have been added to create a coherent mixed-age unit - Smaller
1. Write an equation in slope-point for this line.
1. Write an equation in slope-point for this line. 2. Which of the following equations describes the linear relation graphed below? I II! " 2 3 % & 2! ' 4 " 2 )% ' 3* 3 III 3% ' 2! & 2 " 0 A. I, II, and
Day 1. Last Night s Homework Angle Worksheet (11 problems) Bellwork Angle quiz.
Course: 7 th Grade Math DETAIL LESSON PLAN Wednesday, January 25 / Thursday, January 26 Student Objective (Obj. 3e) TSW use the Pythagorean Theorem to find the missing length of a side of a right triangle.
Lesson 6.1 Skills Practice
Lesson 6.1 Skills Practice Name Date Soon You Will Determine the Right Triangle Connection The Pythagorean Theorem Vocabulary Match each definition to its corresponding term. 1. A mathematical statement
The Pythagorean Theorem is used in many careers on a regular basis. Construction
Applying the Pythagorean Theorem Lesson 2.5 The Pythagorean Theorem is used in many careers on a regular basis. Construction workers and cabinet makers use the Pythagorean Theorem to determine lengths