Section 2.3 Sine Law. Find a. Mar 10 2:23 PM. In grade 10 all triangle were right angle triangles. This will not be the case in grade 11. B B. vs.
|
|
|
- Alicia Lloyd
- 5 years ago
- Views:
Transcription
1 Section 2.3 Filled in KUP.noteook Section 2.3 Sine Law Review Find Find a Mar 10 2:23 PM In grade 10 all triangle were right angle triangles. This will not e the case in grade 11. vs. Mar 10 2:27 PM 1
2 Section 2.3 Filled in KUP.noteook Proof of Sine Law (p.102) Oct 7 10:54 M Note: Triangles are not drawn to scale in these slide shows and during tests/assignments, etc.. Mar 10 2:31 PM 2
3 Section 2.3 Filled in KUP.noteook Find x x Mar 10 2:32 PM x Mar 10 3:32 PM 3
4 Section 2.3 Filled in KUP.noteook What if solving for an angle? Oct 7 11:19 M Find angle Oct 7 11:24 M 4
5 Section 2.3 Filled in KUP.noteook Find angle Oct 7 11:29 M Solve the following triangles. a Mar 10 3:41 PM 5
6 Section 2.3 Filled in KUP.noteook. Oct 8 9:53 M Section 2.3 Part 3 The miguous ase am ig u ous Pronunciation: am 'i gy& w&s Function: adjective Etymology: Latin amiguus, from amigere to e undecided, from ami + agere to drive 1 : doutful or uncertain especially from oscurity or indistinctness <eyes of an amiguous color> 2 : capale of eing understood in two or more possile senses or ways <an amiguous smile> <an amiguous term> <a delierately amiguous reply> Oct 8 9:42 PM 6
7 Section 2.3 Filled in KUP.noteook Youtue Oct 8 9:39 PM We are going to draw a triangle. For consistency we will draw it in the following manner. Oct 8 9:44 PM 7
8 Section 2.3 Filled in KUP.noteook Since we will always draw our triangles this way we can find a formula for height. h c a h Sin = h/ h= Sin Oct 8 9:53 PM When the information of a triangle given is side, side, angle, (SS) The amiguous case can occur. Open you ooks to page 105. Oct 8 10:00 PM 8
9 Section 2.3 Filled in KUP.noteook cute ngle: etween 0 and 90 degrees. Otuse ngle: etween 90 and 180 degrees. Oct 8 10:09 PM When angle is acute. h a<h No Solution Oct 8 10:05 PM 9
10 Section 2.3 Filled in KUP.noteook h a = h One solution (it will e a right angle triangle). Oct 8 10:06 PM h a is greater than or equal to. One solution. Oct 8 10:06 PM 10
11 Section 2.3 Filled in KUP.noteook h h h<a< Two Solutions Oct 8 10:07 PM h Oct 8 10:07 PM 11
12 Section 2.3 Filled in KUP.noteook When is otuse. a< No Solution Oct 8 10:09 PM a = No Solution Oct 8 10:16 PM 12
13 Section 2.3 Filled in KUP.noteook a> One Solution Oct 8 10:16 PM Determine the numer of solutions. a. = 40 0 a = 12 = 7. = 35 0 a = 9 = 13 c. = a = 20 = 17 Oct 8 10:19 PM 13
14 Section 2.3 Filled in KUP.noteook Determine the numer of solutions and solve the triangle. a. =30 0 a = 6 = 12 Oct 8 10:33 PM. = 30 0 a = 24 = 42 Oct 8 10:35 PM 14
15 Section 2.3 Filled in KUP.noteook Oct 3 1:30 PM Oct 6 1:55 PM 15
16 Section 2.3 Filled in KUP.noteook Example 1: In, a = 20, c = 16, and m< = 30º. How many distinct triangles can e drawn given these measurements? Find c if it exists, if there are two possile answers give oth answers. Round your answer(s) to the one if necessary. Mar 30 10:38 M Example 2: In, a = 7, c = 16, and m< = 30º. How many distinct triangles can e drawn given these measurements? Find c if it exists, if there are two possile answers give oth answers. Round your answer(s) to the tenth if necessary. Mar 30 11:00 M 16
17 Section 2.3 Filled in KUP.noteook Example 3: In, a = 10, = 16, and m< = 30º. How many distinct triangles can e drawn given these measurements? Find c if it exists, if there are two possile answers give oth answers. Round your answer(s) to the one if necessary. Mar 30 11:01 M Example 4: In, a = 10, = 8, and m< = 40º. How many distinct triangles can e drawn given these measurements? Find c if it exists, if there are two possile answers give oth answers. Round your answer(s) to the one if necessary. Oct 6 1:05 PM 17
18 Section 2.3 Filled in KUP.noteook Example 5: In, a = 10, m< = 30º and m< = 70º. How many distinct triangles can e drawn given these measurements? Find c if it exists, if there are two possile answers give oth answers. Round your answer(s) to the one if necessary. Oct 6 1:08 PM John wants to measure the length of the trunk of a tree. He walks exactly 35 m from the ase of the tree and looks up. The angle from the ground to the top of the tree is This particular tree grows at an angle of 83 0 with respect to the ground rather than vertically. What is the length of the trunk of the tree? Round off the answer to one decimal place. Oct 6 1:11 PM 18
19 Section 2.3 Filled in KUP.noteook hot air alloon is flying aove harlottetown. Mr. MacDougald is standing due west of the alloon and can see the alloon at an angle of inclination of Mrs. Smith is due east of the alloon and sees the alloon at an angle of inclination of If Mr. MacDougald and Mrs. Smith are 800 m apart horizontally, how far is the alloon from Mr. MacDougald? Oct 6 1:18 PM chandelier is suspended from a horizontal eam y two support chains. One of the chains is 4.5 m long and forms an angle of 63 0 with the eam. If the second chain is 5.8 m long what is the angle it forms with the eam? Round your answer to the one. Oct 6 1:22 PM 19
20 Section 2.3 Filled in KUP.noteook Oct 6 1:29 PM 20
UNIT 10 Trigonometry UNIT OBJECTIVES 287
UNIT 10 Trigonometry Literally translated, the word trigonometry means triangle measurement. Right triangle trigonometry is the study of the relationships etween the side lengths and angle measures of
Chapter 6. Additional Topics in Trigonometry. 6.1 The Law of Sines. Copyright 2014, 2010, 2007 Pearson Education, Inc.
Chapter 6 dditional Topics in Trigonometry 6.1 The Law of Sines Copyright 2014, 2010, 2007 Pearson Education, Inc. 1 Objectives: Use the Law of Sines to solve oblique triangles. Use the Law of Sines to
Name: Class: Date: Chapter 3 - Foundations 7. Multiple Choice Identify the choice that best completes the statement or answers the question.
Name: Class: Date: Chapter 3 - Foundations 7 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Determine the value of tan 59, to four decimal places. a.
Chapter 6 Review. Extending Skills with Trigonometry. Check Your Understanding
hapter 6 Review Extending Skills with Trigonometry heck Your Understanding. Explain why the sine law holds true for obtuse angle triangles as well as acute angle triangles. 2. What dimensions of a triangle
Ready To Go On? Skills Intervention 8-1 Similarity in Right Triangles
8 Find this vocabular word in Lesson 8-1 and the Multilingual Glossar. Finding Geometric Means The geometric mean of two positive numbers is the positive square root of their. Find the geometric mean of
Preview: Correctly fill in the missing side lengths (a, b, c) or the missing angles (α, β, γ) on the following diagrams.
Preview: Correctly fill in the missing side lengths (a, b, c) or the missing angles (α, β, γ) on the following diagrams. γ b a β c α Goal: In chapter 1 we were given information about a right triangle
14.1 Similar Triangles and the Tangent Ratio Per Date Trigonometric Ratios Investigate the relationship of the tangent ratio.
14.1 Similar Triangles and the Tangent Ratio Per Date Trigonometric Ratios Investigate the relationship of the tangent ratio. Using the space below, draw at least right triangles, each of which has one
Unit 5 Day 5: Law of Sines and the Ambiguous Case
Unit 5 Day 5: Law of Sines and the Ambiguous Case Warm Up: Day 5 Draw a picture and solve. Label the picture with numbers and words including the angle of elevation/depression and height/length. 1. The
Lesson #64 First Degree Trigonometric Equations
Lesson #64 First Degree Trigonometric Equations A2.A.68 Solve trigonometric equations for all values of the variable from 0 to 360 How is the acronym ASTC used in trigonometry? If I wanted to put the reference
Acute Angles and Right Triangles. Copyright 2017, 2013, 2009 Pearson Education, Inc.
2 Acute Angles and Right Triangles Copyright 2017, 2013, 2009 Pearson Education, Inc. 1 2.5 Further Applications of Right Triangles Historical Background Bearing Further Applications Copyright 2017, 2013,
( ) ( ) = π r Circumference: 2. Honors Geometry B Exam Review. Areas of Polygons. 1 A = bh Rectangle: A bh 2. Triangle: = Trapezoid: = ( + )
reas of Polygons Triangle: 1 = bh Rectangle: bh 1 b1 b h = Trapezoid: = ( + ) Parallelogram: = bh Regular Polygon: 1 1 = ap = apothem perimeter Coordinate Geometry y y1 Slope: Circles 1 1 1 Midpoint: +,
MEP Practice Book ES4. b 4 2
4 Trigonometr MEP Practice ook ES4 4.4 Sine, osine and Tangent 1. For each of the following triangles, all dimensions are in cm. Find the tangent ratio of the shaded angle. c b 4 f 4 1 k 5. Find each of
Chapter 7. Right Triangles and Trigonometry
hapter 7 Right Triangles and Trigonometry 7.1 pply the Pythagorean Theorem 7.2 Use the onverse of the Pythagorean Theorem 7.3 Use Similar Right Triangles 7.4 Special Right Triangles 7.5 pply the Tangent
(13) Page #1 8, 12, 13, 15, 16, Even, 29 32, 39 44
Geometry/Trigonometry Unit 7: Right Triangle Notes Name: Date: Period: # (1) Page 430 #1 15 (2) Page 430 431 #16 23, 25 27, 29 and 31 (3) Page 437 438 #1 8, 9 19 odd (4) Page 437 439 #10 20 Even, 23, and
Chapter 8 Diagnostic Test
Chapter 8 Diagnostic Test STUDENT BOOK PAGES 422 455 1. Determine the measures of the indicated angles in each diagram. b) 2. Determine the value of each trigonometric ratio to four decimal places. sin
MAP4CI Date Lesson Text Assigned Work Done Ref. Pythagorean Theorem, Pg 72 # 4-7, 9,10 ab P9 93 # 3, 6, 10, 11, 12
MAP4CI 2015-2016 Name: Trigonometry Unit 2 Outline Reminder: Write a missed Quiz or Test in room 540 at lunch or on your spare on the first day of return to school. If you have any concerns, please see
Youngstown State University Trigonometry Final Exam Review (Math 1511)
Youngstown State University Trigonometry Final Exam Review (Math 1511) 1. Convert each angle measure to decimal degree form. (Round your answers to thousandths place). a) 75 54 30" b) 145 18". Convert
2.1 The Tangent Ratio
2.1 The Tangent Ratio C 2.1 Concept: 14, 15 PreAP FPCM 10 (Ms. Carignan) Outcome FP10.4 Trigonometry Chapter 2 Page 1 PreAP FPCM 10 (Ms. Carignan) Outcome FP10.4 Trigonometry Chapter 2 Page 2 Online Video
Math 1201 Chapter 2 Review
ath 1201 hapter 2 Review ultiple hoice Identify the choice that best completes the statement or answers the question. 1. etermine tan and tan. 8 10 a. tan = 1.25; tan = 0.8 c. tan = 0.8; tan = 1.25 b.
National 5 Portfolio Relationships 1.5 Trig equations and Graphs
National 5 Portfolio Relationships 1.5 Trig equations and Graphs N5 Section A - Revision This section will help you revise previous learning which is required in this topic. R1 I can use Trigonometry in
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Precalculus CP Final Exam Review - 01 Name Date: / / MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Convert the angle in degrees to radians. Express
Chapter 4: Triangle and Trigonometry
Chapter 4: Triangle and Trigonometry Paper 1 & 2B 3.1.3 Triangles 3.1.3 Triangles 2A Understand a proof of Pythagoras Theorem. Understand the converse of Pythagoras Theorem. Use Pythagoras Trigonometry
Theorem 8-1-1: The three altitudes in a right triangle will create three similar triangles
G.T. 7: state and apply the relationships that exist when the altitude is drawn to the hypotenuse of a right triangle. Understand and use the geometric mean to solve for missing parts of triangles. 8-1
Name: Unit 8 Right Triangles and Trigonometry Unit 8 Similarity and Trigonometry. Date Target Assignment Done!
Unit 8 Similarity and Trigonometry Date Target Assignment Done! M 1-22 8.1a 8.1a Worksheet T 1-23 8.1b 8.1b Worksheet W 1-24 8.2a 8.2a Worksheet R 1-25 8.2b 8.2b Worksheet F 1-26 Quiz Quiz 8.1-8.2 M 1-29
Name: Block: What I can do for this unit:
Unit 8: Trigonometry Student Tracking Sheet Math 10 Common Name: Block: What I can do for this unit: After Practice After Review How I Did 8-1 I can use and understand triangle similarity and the Pythagorean
These are the type of problems that you will be working on in class. These problems are from Lesson 7.
Pre-Class Problems 10 for Wednesda, October 10 These are the tpe of problems that ou will be working on in class. These problems are from Lesson 7. Solution to Problems on the Pre-Eam. You can go to the
1/2/2018. Unit 4.7: The Law of Sines and The Law of Cosines. Warm-Up. Triangle That Just Aren t Right
Warm-Up Example 7. A building is 60 ft high. From a distance at point A on the ground, the angle of elevation to the top of the building is 40º. From a little nearer at point B, the angle of elevation
Section 3.2 Quadratic Functions
3. Quadratic Functions 163 Section 3. Quadratic Functions In this section, we will explore the family of nd degree polynomials, the quadratic functions. While they share many characteristics of polynomials
Section 10.6 Right Triangle Trigonometry
153 Section 10.6 Right Triangle Trigonometry Objective #1: Understanding djacent, Hypotenuse, and Opposite sides of an acute angle in a right triangle. In a right triangle, the otenuse is always the longest
Non Right Triangle Vector Addition. Sections 1.7 and 1.8
Non Right Triangle Vector Addition Sections 1.7 and 1.8 Question: Why in the name of all that is good would someone want to do something like THAT? Answer: Because there is no law that states vectors must
T.4 Applications of Right Angle Trigonometry
22 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, navigators,
Chapter 2 Trigonometry
Foundations of Math 11 Chapter 2 Note Package Chapter 2 Lesson 1 Review (No Practice Questions for this Lesson) Page 1 The Beauty of Triangles (No Notes for this Page) Page 2 Pythagoras Review (No Notes
You will need the following items: scissors, plate, 5 different colored pencils, protractor, paper to answer questions
Radian measure task You will need the following items: scissors, plate, 5 different colored pencils, protractor, paper to answer questions Instructions will follow on each slide. Feb 19 10:33 AM Step 1
: Find the values of the six trigonometric functions for θ. Special Right Triangles:
ALGEBRA 2 CHAPTER 13 NOTES Section 13-1 Right Triangle Trig Understand and use trigonometric relationships of acute angles in triangles. 12.F.TF.3 CC.9- Determine side lengths of right triangles by using
Packet Unit 5 Trigonometry Honors Math 2 17
Packet Unit 5 Trigonometry Honors Math 2 17 Homework Day 12 Part 1 Cumulative Review of this unit Show ALL work for the following problems! Use separate paper, if needed. 1) If AC = 34, AB = 16, find sin
Grade 6 Math Circles February 29, D Geometry
1 Universit of Waterloo Facult of Mathematics Centre for Education in Mathematics and Computing Grade 6 Math Circles Feruar 29, 2012 2D Geometr What is Geometr? Geometr is one of the oldest ranches in
Pre-Calculus Right Triangle Trigonometry Review Name Dec π
Pre-Calculus Right Triangle Trigonometry Review Name Dec 201 Convert from Radians to Degrees, or Degrees to Radians 7π 1. 0 2.. 1. 11π. Find the si trig functions of θ. If sin θ =, find the other five
Precalculus CP Final Exam Review. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Precalculus CP Final Eam Review Name Date: / / MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Convert the angle in degrees to radians. Epress answer
Practice For use with pages
9.1 For use with pages 453 457 Find the square roots of the number. 1. 36. 361 3. 79 4. 1089 5. 4900 6. 10,000 Approimate the square root to the nearest integer. 7. 39 8. 85 9. 105 10. 136 11. 17.4 1.
a + b2 = c2 thirdside a b sin A sin B sin C one opposite angle other opposite a2 = b2 + 2bccos QHI. F-i. fr+c a - 2bc angle cosa= I ol o =
Angle of elevation is always measured UP from the HORIZONTAL. Angle of depression always measured DOWN from the HORIZONTAL. - given asked asked MAP 4C1 Triconometry Reference Sheet Formula Picture When
While you wait: Without consulting any resources or asking your friends write down everthing you remember about the:
While you wait: Without consulting any resources or asking your friends write down everthing you remember about the: Copyright 2007 Pearson Education, Inc. Slide 10-1 Sec 9.3 The Law of Sines Oblique Triangles
Mathematics (www.tiwariacademy.com)
() Miscellaneous Exercise on Chapter 10 Question 1: Find the values of k for which the line is (a) Parallel to the x-axis, (b) Parallel to the y-axis, (c) Passing through the origin. Answer 1: The given
The cosine ratio is a ratio involving the hypotenuse and one leg (adjacent to angle) of the right triangle Find the cosine ratio for. below.
The Cosine Ratio The cosine ratio is a ratio involving the hypotenuse and one leg (adjacent to angle) of the right triangle. From the diagram to the right we see that cos C = This means the ratio of the
Name Class Date. Essential question: How do you find the tangent, sine, and cosine ratios for acute angles in a right triangle?
Name lass Date 8-2 Trigonometric Ratios Going Deeper Essential question: How do you find the tangent, sine, and cosine ratios for acute angles in a right triangle? In this chapter, you will be working
Packet Unit 5 Right Triangles Honors Common Core Math 2 1
Packet Unit 5 Right Triangles Honors Common Core Math 2 1 Day 1 HW Find the value of each trigonometric ratio. Write the ratios for sinp, cosp, and tanp. Remember to simplify! 9. 10. 11. Packet Unit 5
MCR3U UNIT #6: TRIGONOMETRY
MCR3U UNIT #6: TRIGONOMETRY SECTION PAGE NUMBERS HOMEWORK Prerequisite p. 0 - # 3 Skills 4. p. 8-9 #4, 5, 6, 7, 8, 9,, 4. p. 37 39 #bde, acd, 3, 4acde, 5, 6ace, 7, 8, 9, 0,, 4.3 p. 46-47 #aef,, 3, 4, 5defgh,
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Convert the angle to decimal degrees and round to the nearest hundredth of a degree. 1)
Unit 8 Chapter 3 Properties of Angles and Triangles
Unit 8 Chapter 3 Properties of Angles and Triangles May 16 7:01 PM Types of lines 1) Parallel Lines lines that do not (and will not) cross each other are labeled using matching arrowheads are always the
Name Class Date. Investigating a Ratio in a Right Triangle
Name lass Date Trigonometric Ratios Going Deeper Essential question: How do you find the tangent, sine, and cosine ratios for acute angles in a right triangle? In this chapter, you will be working etensively
Assignment Guide: Chapter 8 Geometry (L3)
Assignment Guide: Chapter 8 Geometry (L3) (91) 8.1 The Pythagorean Theorem and Its Converse Page 495-497 #7-31 odd, 37-47 odd (92) 8.2 Special Right Triangles Page 503-504 #7-12, 15-20, 23-28 (93) 8.2
Find sin R and sin S. Then find cos R and cos S. Write each answer as a fraction and as a decimal. Round to four decimal places, if necessary.
Name Homework Packet 7.6 7.7 LESSON 7.6 For use with pages 473-480 AND LESSON 7.7 For use with pages 483 489 Find sin R and sin S. Then find cos R and cos S. Write each answer as a fraction and as a decimal.
Angles of a Triangle. Activity: Show proof that the sum of the angles of a triangle add up to Finding the third angle of a triangle
Angles of a Triangle Activity: Show proof that the sum of the angles of a triangle add up to 180 0 Finding the third angle of a triangle Pythagorean Theorem Is defined as the square of the length of the
UNIT 9 - RIGHT TRIANGLES AND TRIG FUNCTIONS
UNIT 9 - RIGHT TRIANGLES AND TRIG FUNCTIONS Converse of the Pythagorean Theorem Objectives: SWBAT use the converse of the Pythagorean Theorem to solve problems. SWBAT use side lengths to classify triangles
Trigonometric Graphs
GCSE MATHEMATICS Trigonometric Graphs X These questions have been taken or modified from previous AQA GCSE Mathematics Papers. Instructions Use black ink or black ball-point pen. Draw diagrams in pencil.
Solving Right Triangles. How do you solve right triangles?
Solving Right Triangles How do you solve right triangles? The Trigonometric Functions we will be looking at SINE COSINE TANGENT The Trigonometric Functions SINE COSINE TANGENT SINE Pronounced sign TANGENT
Ch 7 & 8 Exam Review. Note: This is only a sample. Anything covered in class or homework may appear on the exam.
Ch 7 & 8 Exam Review Note: This is only a sample. Anything covered in class or homework may appear on the exam. Determine whether there is sufficient information for solving a triangle, with the given
4.1 Reviewing the Trigonometry of Right Triangles
4.1 Reviewing the Trigonometry of Right Triangles INVSTIGT & INQUIR In the short story The Musgrave Ritual, Sherlock Holmes found the solution to a mystery at a certain point. To find the point, he had
a. b. c. d. e. f. g. h.
Sec. Right Triangle Trigonometry Right Triangle Trigonometry Sides Find the requested unknown side of the following triangles. Name: a. b. c. d.? 44 8 5? 7? 44 9 58 0? e. f. g. h.?? 4 7 5? 38 44 6 49º?
Chapter 7: Right Triangles and Trigonometry Name: Study Guide Block: Section and Objectives
Page 1 of 22 hapter 7: Right Triangles and Trigonometr Name: Stud Guide lock: 1 2 3 4 5 6 7 8 SOL G.8 The student will solve real-world problems involving right triangles b using the Pthagorean Theorem
10-2. More Right-Triangle Trigonometry. Vocabulary. Finding an Angle from a Trigonometric Ratio. Lesson
hapter 10 Lesson 10-2 More Right-Triangle Trigonometry IG IDE If you know two sides of a right triangle, you can use inverse trigonometric functions to fi nd the measures of the acute angles. Vocabulary
You ll use the six trigonometric functions of an angle to do this. In some cases, you will be able to use properties of the = 46
Math 1330 Section 6.2 Section 7.1: Right-Triangle Applications In this section, we ll solve right triangles. In some problems you will be asked to find one or two specific pieces of information, but often
Cumulative Review: SOHCAHTOA and Angles of Elevation and Depression
Cumulative Review: SOHCAHTOA and Angles of Elevation and Depression Part 1: Model Problems The purpose of this worksheet is to provide students the opportunity to review the following topics in right triangle
Unit 5 Day 4: Law of Sines & Area of Triangles with Sines
Unit 5 Day 4: Law of Sines & Area of Triangles with Sines Warm-up: Draw a picture and solve. Label the picture with numbers and words including the angle of elevation/depression and height/length. 1. A
Solving Problems with Similar Triangles
Solving Problems with Similar Triangles xample 1: Given that lines and are parallel in the figure to the right, determine the value of x, the distance between points and. Solution: First, we can demonstrate
Lesson 26 - Review of Right Triangle Trigonometry
Lesson 26 - Review of Right Triangle Trigonometry PreCalculus Santowski PreCalculus - Santowski 1 (A) Review of Right Triangle Trig Trigonometry is the study and solution of Triangles. Solving a triangle
You ll use the six trigonometric functions of an angle to do this. In some cases, you will be able to use properties of the = 46
Math 1330 Section 6.2 Section 7.1: Right-Triangle Applications In this section, we ll solve right triangles. In some problems you will be asked to find one or two specific pieces of information, but often
1. (10 pts.) Find and simplify the difference quotient, h 0for the given function
MATH 1113/ FALL 016 FINAL EXAM Section: Grade: Name: Instructor: f ( x h) f ( x) 1. (10 pts.) Find and simplify the difference quotient, h 0for the given function h f ( x) x 5. (10 pts.) The graph of the
1/2/2018. Unit 4.7: The Law of Sines and The Law of Cosines. Warm-Up. Triangle That Just Aren t Right. Apply the Law of Sines (AAS) Real world example
Warm-Up Example 7. A building is 60 ft high. From a distance at point A on the ground, the angle of elevation to the top of the building is 40º. From a little nearer at point B, the angle of elevation
Math B Regents Exam 0603 Page b For which value of x is y = log x undefined?
Math B Regents Exam 0603 Page 1 1. 060301b For which value of x is y = log x undefined? [A] 1 10. 06030b, P.I. A.A.58 [B] 1483. [C] π [D] 0 If sinθ > 0 and sec θ < 0, in which quadrant does the terminal
6.2 Similar Triangles
6. Similar Triangles MTHPOW TM 10, Ontario dition, pp. 318 35 If and are similar, a) the corresponding pairs of angles are equal = = = the ratios of the corresponding sides are equal a b c = = d e f c)
Skills Practice Skills Practice for Lesson 7.1
Skills Practice Skills Practice for Lesson.1 Name Date Tangent Ratio Tangent Ratio, Cotangent Ratio, and Inverse Tangent Vocabulary Match each description to its corresponding term for triangle EFG. F
Section The Law of Sines and the Law of Cosines
Section 7.3 - The Law of Sines and the Law of Cosines Sometimes you will need to solve a triangle that is not a right triangle. This type of triangle is called an oblique triangle. To solve an oblique
You know that the circumference of a specific circle divided by its diameter is the ratio pi, written as.
Unit 6, Lesson.1 Circumference and Area of a Circle You have used the formulas for finding the circumference and area of a circle. In this lesson, you will prove why the formulas for circumference and
1. What is cos(20 ) csc(70 )? This is a review of the complementary angle theorem that you learned about last time.
Math 121 (Lesieutre); 8.1, cont.; Novemer 10, 2017 1. What is cos(20 ) csc(70 )? This is a review of the complementary angle theorem that you learned aout last time. cos(20 ) csc(70 ) = cos(20 ) sec(90
Home Lab 7 Refraction, Ray Tracing, and Snell s Law
Home Lab Week 7 Refraction, Ray Tracing, and Snell s Law Home Lab 7 Refraction, Ray Tracing, and Snell s Law Activity 7-1: Snell s Law Objective: Verify Snell s law Materials Included: Laser pointer Cylindrical
Math Analysis Final Exam Review. Chapter 1 Standards
Math Analysis Final Exam Review Chapter 1 Standards 1a 1b 1c 1d 1e 1f 1g Use the Pythagorean Theorem to find missing sides in a right triangle Use the sine, cosine, and tangent functions to find missing
Math 144 Activity #3 Coterminal Angles and Reference Angles
144 p 1 Math 144 Activity #3 Coterminal Angles and Reference Angles For this activity we will be referring to the unit circle. Using the unit circle below, explain how you can find the sine of any given
Inverses of Trigonometric. Who uses this? Hikers can use inverse trigonometric functions to navigate in the wilderness. (See Example 3.
1-4 Inverses of Trigonometric Functions Objectives Evaluate inverse trigonometric functions. Use trigonometric equations and inverse trigonometric functions to solve problems. Vocabulary inverse sine function
7.2 Isosceles and Equilateral Triangles
Name lass Date 7.2 Isosceles and Equilateral Triangles Essential Question: What are the special relationships among angles and sides in isosceles and equilateral triangles? Resource Locker Explore G.6.D
Advanced Math Final Exam Review Name: Bornoty May June Use the following schedule to complete the final exam review.
Advanced Math Final Exam Review Name: Bornoty May June 2013 Use the following schedule to complete the final exam review. Homework will e checked in every day. Late work will NOT e accepted. Homework answers
Geometry B Midterm REVIEW
Geometr Midterm REVIEW Name HR: 1. The measures of the angles of a triangle are in the etended ratio 2 : 3 : 7. What is the measure of the largest angle? 2. The ratio of length to width in a rectangle
Warm Up: please factor completely
Warm Up: please factor completely 1. 2. 3. 4. 5. 6. vocabulary KEY STANDARDS ADDRESSED: MA3A2. Students will use the circle to define the trigonometric functions. a. Define and understand angles measured
Non-right Triangles: Law of Cosines *
OpenStax-CNX module: m49405 1 Non-right Triangles: Law of Cosines * OpenStax This work is produced by OpenStax-CNX and licensed under the Creative Commons Attribution License 4.0 In this section, you will:
Assignment. Pg. 567 #16-33, even pg 577 # 1-17 odd, 32-37
Assignment Intro to Ch. 8 8.1 8. Da 1 8. Da 8. Da 1 8. Da Review Quiz 8. Da 1 8. Da 8. Etra Practice 8.5 8.5 In-class project 8.6 Da 1 8.6 Da Ch. 8 review Worksheet Worksheet Worksheet Worksheet Worksheet
Precalculus eday #3 Assignment
Name Date Score Precalculus eday #3 Assignment 1. If X = 35, Y = 84, and Z = 91, what is the cosine of B? 2. If X = 60, Y = 25, and Z = 65, what is the sine of B? 3. In the triangle shown above m A = 43,
HW. Pg. 334 #1-9, 11, 12 WS. A/ Angles in Standard Position: Terminology: Initial Arm. Terminal Arm. Co-Terminal Angles. Quadrants
MCR 3UI Introduction to Trig Functions Date: Lesson 6.1 A/ Angles in Standard Position: Terminology: Initial Arm HW. Pg. 334 #1-9, 11, 1 WS Terminal Arm Co-Terminal Angles Quadrants Related Acute Angles
MATH 122 Final Exam Review Precalculus Mathematics for Calculus, 7 th ed., Stewart, et al
MATH Final Eam Review Precalculus Mathematics for Calculus, 7 th ed., Stewart, et al.. Mark the point determined by on the unit circle... Sketch a graph of y = sin( ) by hand... Find the amplitude, period,
SECTION 7.4 THE LAW OF SINES 483. Triangles AjfijC, and A2B2C2 are shown in Figure 9. b = a = EXAMPLE 5 SSA, the No-Solution Case
SECTION 7.4 THE LAW OF SINES 483 the foothills of the Himalayas. A later expedition, using triangulation, calculated the height of the highest peak of the Himalayas to be 29,002 ft. The peak was named
4-1 Right Triangle Trigonometry
Find the exact values of the six trigonometric functions of θ. 1. sin θ =, cos θ =, tan θ =, csc θ 5. sin θ =, cos θ =, tan θ =, csc θ =, sec θ =, cot θ = =, sec θ =, cot θ = 2. sin θ =, cos θ =, tan θ
5.5 Right Triangles. 1. For an acute angle A in right triangle ABC, the trigonometric functions are as follow:
5.5 Right Triangles 1. For an acute angle A in right triangle ABC, the trigonometric functions are as follow: sin A = side opposite hypotenuse cos A = side adjacent hypotenuse B tan A = side opposite side
UNIT 3 CIRCLES AND VOLUME Lesson 5: Explaining and Applying Area and Volume Formulas Instruction
Prerequisite Skills This lesson requires the use of the following skills: using formulas for the surface areas of polygons and circles performing calculations with the angles in circles using the Pythagorean
Congruence and Similarity in Triangles Pg. 378 # 1, 4 8, 12. Solving Similar Triangle Problems Pg. 386 # 2-12
UNIT 7 SIMILAR TRIANGLES AND TRIGONOMETRY Date Lesson TOPIC Homework May 4 7.1 7.1 May 8 7.2 7.2 Congruence and Similarity in Triangles Pg. 378 # 1, 4 8, 12 Solving Similar Triangle Problems Pg. 386 #
Day 4 Trig Applications HOMEWORK
Day 4 Trig Applications HOMEWORK 1. In ΔABC, a = 0, b = 1, and mc = 44º a) Find the length of side c to the nearest integer. b) Find the area of ΔABC to the nearest tenth.. In ΔABC, ma = 50º, a = 40, b
Right Triangle Trigonometry
Right Triangle Trigonometry 1 The six trigonometric functions of a right triangle, with an acute angle, are defined by ratios of two sides of the triangle. hyp opp The sides of the right triangle are:
Intro Right Triangle Trig
Ch. Y Intro Right Triangle Trig In our work with similar polygons, we learned that, by definition, the angles of similar polygons were congruent and their sides were in proportion - which means their ratios
Solve the following system of equations using either substitution or elimination:
Mathematics 04 Final Eam Review Topic : Solving a system of equations in three variables. 009 Solve the following system of equations using either substitution or elimination: + y + z 0 + y z y + z Select
7.1/7.2 Apply the Pythagorean Theorem and its Converse
7.1/7.2 Apply the Pythagorean Theorem and its Converse Remember what we know about a right triangle: In a right triangle, the square of the length of the is equal to the sum of the squares of the lengths
1) The domain of y = sin-1x is The range of y = sin-1x is. 2) The domain of y = cos-1x is The range of y = cos-1x is
MAT 204 NAME TEST 4 REVIEW ASSIGNMENT Sections 8.1, 8.3-8.5, 9.2-9.3, 10.1 For # 1-3, fill in the blank with the appropriate interval. 1) The domain of y = sin-1x is The range of y = sin-1x is 2) The domain
Park Forest Math Team. Meet #3. Geometry. Self-study Packet
Park Forest Math Team Meet #3 Self-study Packet Problem Categories for this Meet: 1. Mystery: Problem solving 2. : ngle measures in plane figures including supplements and complements 3. Number Theory:
Find the length, x, in the diagram, rounded to the nearest tenth of a centimetre.
The tangent ratio relates two sides of a right triangle and an angle. If ou know an angle and the length of one of the legs of the triangle, ou can find the length of the other leg. Eample Find a Side