Trigonometric Functions
|
|
|
- Roger Johns
- 5 years ago
- Views:
Transcription
1 Trigonometric Functions (Chapters 6 & 7, 10.1, 10.2) E. Law of Sines/Cosines May 21-12:26 AM May 22-9:52 AM 1
2 degree measure May 22-9:52 AM Measuring in Degrees (360 degrees) is the angle obtained when rotating a Right Angle Jan 21-11:11 PM 2
3 θ, in radians. Jan 16-9:55 PM Jan 16-10:26 PM 3
4 "in radians" radians: Jan 16-10:27 PM Ex: Convert to degrees Jan 22-10:23 PM 4
5 Jan 22-10:25 PM May 22-9:42 PM 5
6 Jan 22-10:32 PM Jan 22-10:27 PM 6
7 Ex 2: Find the angle of the sector when: a). radius is 4.3 m and arc length is 2.95m b). radius is 10 cm and area is 30 cm 2 Jan 7-10:04 AM Angular & Linear Speed rpm (revolutions per minute) Angular speed If the wheel rotates an angle on the rotating wheel travels a distance in May 23-9:26 PM 7
8 Jan 22-10:58 PM Recall: Ex: Find the missing side. Remark: Since the right triangle has a 90 angles must be. Jan 3-2:55 PM 8
9 Hypotenuse Opposite Jan 3-2:55 PM Six Trigonometric Functions Jan 3-7:20 PM 9
10 Hypotenuse Opposite Jan 3-3:16 PM SOH-CAH-TOA Jan 3-3:16 PM 10
11 Jan 3-7:43 PM Right Triangle Proof: Start with any equilateral triangle. Why? 1 1 h h 1 h Jan 7-10:59 AM 11
12 Right Triangle Consequences: Jan 7-10:59 AM csc30 Jan 3-9:50 PM 12
13 Jan 3-9:57 PM Right Triangle Proof: Start with any isosceles right triangle. Why? x x 1 x h x Jan 7-10:59 AM 13
14 Right Triangle x h Consequences: x Jan 7-10:59 AM We found 45º 45º 45º 45º csc45 Jan 3-8:04 PM 14
15 /6 /4 /3 May 23-10:40 PM 2) cos53 5) sec53 Jan 3-10:09 PM 15
16 May 27-10:11 PM May 27-10:16 PM 16
17 Jan 3-10:15 PM Jan 8-11:34 AM 17
18 Jan 8-12:02 PM Ex: (Application) The base of the tree is 65 feet from point P & the angle of elevation to the top of the tree is 41º. Find the height of Jan 8-12:04 PM 18
19 base b is given by b θ. Jan 8-12:05 PM Jan 8-12:14 PM 19
20 Jan 8-12:19 PM C. Trigonometry of Angles: Negative Angle (Clockwise) May 25-12:05 AM 20
21 May 25-7:40 PM Remark: Just as we discussed clockwise would represent a Jan 8-2:34 PM 21
22 sinθ = sinθ = May 25-7:34 PM where it intersects unit circle. Jan 8-2:46 PM 22
23 The terminal pt ( 3/5, 4/5) is a point on the unit circle that corresponds to an angle Jan 8-6:04 PM θ (in standard position) meets the unit circle. Use info to find the Jan 22-10:59 PM 23
24 Jan 8-6:06 PM Jan 8-6:38 PM 24
25 sin π/6 π/4 π/3 π/2 sin Jan 8-6:54 PM Unit Circle in degrees and radians Jan 8-6:47 PM 25
26 Tip to memorize Jan 8-6:51 PM Tip to memorize Jan 8-6:51 PM 26
27 Tip to memorize Jan 8-6:51 PM Tip to memorize Jan 8-6:51 PM 27
28 Unit Circle in degrees and radians Jan 8-6:47 PM θ = π θ = -π/2 Jan 22-11:19 PM 28
29 Jan 8-6:49 PM θ. Jan 8-6:49 PM 29
30 Jan 8-8:10 PM Jan 8-8:17 PM 30
31 Jan 8-8:47 PM References to Jan 22-11:38 PM 31
32 Jan 23-10:57 PM 1) Reference of 2 cos(2 2) Reference of -5 cos(-5 Jan 23-10:39 PM 32
33 Jan 23-11:05 PM The Complete Unit Circle - Memorize this! Jan 16-12:33 PM 33
34 & Recall: other trig functions" (Need to memorize!) May 27-10:21 PM trigonometric functions. 0 0, find remaining Jan 8-8:49 PM 34
35 trigonometric functions. 0 0, find remaining May 27-10:51 PM trigonometric functions. 0 0, find remaining May 27-10:51 PM 35
36 Jan 8-8:59 PM Remark: Given Ex. Derive similar identities for the other four trig functions. May 27-11:03 PM 36
37 Trigonometric Proofs How to 'do' proofs: We use a combination of algebra and basic identities along with the following guidelines: Guidelines for Proving Trig Identities 1) Start with one side. - Start w/ most complicated side - You may work with both sides if stuck. 2) Use known Identities Jan 29-10:02 PM A(1 + cot Guidelines for Proving Trig Identities 1) Start with one side. - Start w/ most complicated side - You may work with both sides if stuck. 2) Use known Identities Jan 29-10:02 PM 37
38 Jan 8-9:05 PM Jan 8-9:02 PM 38
39 = 2 + 2cot Jan 29-10:03 PM Trigonometric Algebra Ex: Simplify Jan 29-9:05 PM 39
40 1 + cos Jan 29-9:59 PM cot csc Jan 29-10:00 PM 40
41 Recall: The Complete Unit Circle May 21-12:18 AM Skill: Can you think "backwards" from the unit circle? Ex. Find the angle that satisfies the trig value: May 21-12:18 AM 41
42 θ = ) cosθ = Aug 5-7:42 PM May 21-12:18 AM 42
43 1) (SAA) May 25-11:13 AM 2) (ASA) May 25-11:31 AM 43
44 May 25-9:54 PM 4) (SSA) a = 5 May 25-10:18 PM 44
45 3) (SSA) a = 7 May 25-10:18 PM May 25-11:34 AM 45
46 + c - 2bccosA + c - 2accosB - 2abcosC May 25-10:20 PM 1) (SSS) May 25-10:59 PM 46
47 2) (SAS) May 25-11:03 PM EX 2: The end wall of a building has the shape illustrated, where the center of arc AB is at C. Find: a). to 4 significant digits b) to 4 significant digits c) the area of the wall Jan 7-10:12 AM 47
Application of Geometric Mean
Section 8-1: Geometric Means SOL: None Objective: Find the geometric mean between two numbers Solve problems involving relationships between parts of a right triangle and the altitude to its hypotenuse
Use SOH CAH TOA to memorize the three main trigonometric functions.
Use SOH CAH TOA to memorize the three main trigonometric functions. Content Objective Content Objective Content Objective Content Objective Content Objective Content Objective Content Objective Content
The statements of the Law of Cosines
MSLC Workshop Series: Math 1149 and 1150 Law of Sines & Law of Cosines Workshop There are four tools that you have at your disposal for finding the length of each side and the measure of each angle of
8.7 Extension: Laws of Sines and Cosines
www.ck12.org Chapter 8. Right Triangle Trigonometry 8.7 Extension: Laws of Sines and Cosines Learning Objectives Identify and use the Law of Sines and Cosines. In this chapter, we have only applied the
Similar Right Triangles
MATH 1204 UNIT 5: GEOMETRY AND TRIGONOMETRY Assumed Prior Knowledge Similar Right Triangles Recall that a Right Triangle is a triangle containing one 90 and two acute angles. Right triangles will be similar
Chapter 7. Right Triangles and Trigonometry
Chapter 7 Right Triangles and Trigonometry 4 16 25 100 144 LEAVE IN RADICAL FORM Perfect Square Factor * Other Factor 8 20 32 = = = 4 *2 = = = 75 = = 40 = = 7.1 Apply the Pythagorean Theorem Objective:
Lesson 30, page 1 of 9. Glencoe Geometry Chapter 8.3. Trigonometric Ratios
Lesson 30 Lesson 30, page 1 of 9 Glencoe Geometry Chapter 8.3 Trigonometric Ratios Today we look at three special ratios of right triangles. The word Trigonometry is derived from two Greek words meaning
EQ: How do I use trigonometry to find missing side lengths of right triangles?
EQ: How do I use trigonometry to find missing side lengths of right triangles? Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Essential
Geom- Chpt. 8 Algebra Review Before the Chapter
Geom- Chpt. 8 Algebra Review Before the Chapter Solving Quadratics- Using factoring and the Quadratic Formula Solve: 1. 2n 2 + 3n - 2 = 0 2. (3y + 2) (y + 3) = y + 14 3. x 2 13x = 32 1 Working with Radicals-
Special Right Triangles
GEOMETRY Special Right Triangles OBJECTIVE #: G.SRT.C.8 OBJECTIVE Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. *(Modeling Standard) BIG IDEA (Why is
8.1 The Law of Sines Congruency and Oblique Triangles Using the Law of Sines The Ambiguous Case Area of a Triangle
Chapter 8 Applications of Trigonometry 8-1 8.1 The Law of Sines Congruency and Oblique Triangles Using the Law of Sines The Ambiguous Case Area of a Triangle A triangle that is not a right triangle is
Learning Goal: I can explain when to use the Sine, Cosine and Tangent ratios and use the functions to determine the missing side or angle.
MFM2P Trigonometry Checklist 1 Goals for this unit: I can solve problems involving right triangles using the primary trig ratios and the Pythagorean Theorem. U1L4 The Pythagorean Theorem Learning Goal:
Unit 3 Trigonometry. 3.1 Use Trigonometry to Find Lengths
Topic : Goal : Unit 3 Trigonometry trigonometry I can use the primary trig ratios to find the lengths of sides in a right triangle 3.1 Use Trigonometry to Find Lengths In any right triangle, we name the
8.3 Trigonometric Ratios-Tangent. Geometry Mr. Peebles Spring 2013
8.3 Trigonometric Ratios-Tangent Geometry Mr. Peebles Spring 2013 Bell Ringer 3 5 Bell Ringer a. 3 5 3 5 = 3 5 5 5 Multiply the numerator and denominator by 5 so the denominator becomes a whole number.
Name Date Period. (D) 4 π. 3. One revolution per minute is about: (A) rad/s (B) rad/s (C) 0.95 rad/s (D) 1.57 rad/s (E) 6.
Name Date Period Worksheet 5.2 Applications of Angles Show all work. All answers must be given as either simplified, exact answers. A calculator is permitted unless otherwise stated. Unless stated otherwise,
Welcome to Trigonometry!
Welcome to Trigonometry! Right Triangle Trigonometry: The study of the relationship between the sides and the angles of right triangles. Why is this important? I wonder how tall this cake is... 55 0 3
Math Section 4.1 Special Triangles
Math 1330 - Section 4.1 Special Triangles In this section, we ll work with some special triangles before moving on to defining the six trigonometric functions. Two special triangles are 30 60 90 triangles
Unit 2 Day 4 Notes Law of Sines
AFM Unit 2 Day 4 Notes Law of Sines Name Date Introduction: When you see the triangle below on the left and someone asks you to find the value of x, you immediately know how to proceed. You call upon your
EQ: SRT.8 How do I use trig to find missing side lengths of right triangles?
EQ: SRT.8 How do I use trig to find missing side lengths of right triangles? Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Essential
8-1. The Pythagorean Theorem and Its Converse. Vocabulary. Review. Vocabulary Builder. Use Your Vocabulary
8-1 The Pythagorean Theorem and Its Converse Vocabulary Review 1. Write the square and the positive square root of each number. Number 9 Square Positive Square Root 1 4 1 16 Vocabulary Builder leg (noun)
AP Physics 1 Summer Packet Review of Trigonometry used in Physics
AP Physics 1 Summer Packet Review of Trigonometry used in Physics For some of you this material will seem pretty familiar and you will complete it quickly. For others, you may not have had much or any
BASICS OF TRIGONOMETRY
Mathematics Revision Guides Basics of Trigonometry Page 1 of 9 M.K. HOME TUITION Mathematics Revision Guides Level: GCSE Foundation Tier BASICS OF TRIGONOMETRY Version: 1. Date: 09-10-015 Mathematics Revision
UNIT 2 RIGHT TRIANGLE TRIGONOMETRY Lesson 2: Applying Trigonometric Ratios Instruction
Prerequisite Skills This lesson requires the use of the following skills: defining and calculating sine, cosine, and tangent setting up and solving problems using the Pythagorean Theorem identifying the
8-1. The Pythagorean Theorem and Its Converse. Vocabulary. Review. Vocabulary Builder. Use Your Vocabulary
8-1 he Pythagorean heorem and Its Converse Vocabulary Review 1. Write the square and the positive square root of each number. Number Square Positive Square Root 9 81 3 1 4 1 16 1 2 Vocabulary Builder leg
In previous examples of trigonometry we were limited to right triangles. Now let's see how trig works in oblique (not right) triangles.
The law of sines. In previous examples of trigonometry we were limited to right triangles. Now let's see how trig works in oblique (not right) triangles. You may recall from Plane Geometry that if you
Congruence Axioms. Data Required for Solving Oblique Triangles. 1 of 8 8/6/ THE LAW OF SINES
1 of 8 8/6/2004 8.1 THE LAW OF SINES 8.1 THE LAW OF SINES Congrueny and Olique Triangles Derivation of the Law of Sines Appliations Amiguous Case Area of a Triangle Until now, our work with triangles has
Algebra/Geometry Blend Unit #7: Right Triangles and Trigonometry Lesson 1: Solving Right Triangles. Introduction. [page 1]
![Algebra/Geometry Blend Unit #7: Right Triangles and Trigonometry Lesson 1: Solving Right Triangles. Introduction. [page 1]](/thumbs/90/104341621.jpg "Algebra/Geometry Blend Unit #7: Right Triangles and Trigonometry Lesson 1: Solving Right Triangles. Introduction. [page 1]")
Algebra/Geometry Blend Unit #7: Right Triangles and Trigonometry Lesson 1: Solving Right Triangles Name Period Date Introduction [page 1] Learn [page 2] Pieces of a Right Triangle The map Brian and Carla
Gears Ratios and Speed / Problem Solving
Teacher Mechanics Note to the teacher On this page, students will learn about the relationship between gear ratio, gear rotational speed, wheel radius, diameter, circumference, revolutions and distance.
Today we will focus on solving for the sides and angles of non-right triangles when given two angles and a side.
5.5 The Law of Sines: Part 1 Pre-Calculus Learning Targets: 1. Use the Law of Sines to solve non-right triangles. Today we will focus on solving for the sides and angles of non-right triangles when given
Parking Lot HW? Joke of the Day: What do you get when you combine a flat, infinite geometric figure with a beef patty?
Parking Lot HW? Joke of the Day: What do you get when you combine a flat, infinite geometric figure with a beef patty? a plane burger Agenda 1 23 hw? Finish Special Right Triangles L8 3 Trig Ratios HW:
77.1 Apply the Pythagorean Theorem
Right Triangles and Trigonometry 77.1 Apply the Pythagorean Theorem 7.2 Use the Converse of the Pythagorean Theorem 7.3 Use Similar Right Triangles 7.4 Special Right Triangles 7.5 Apply the Tangent Ratio
2.6 Related Rates Worksheet Calculus AB. dy /dt!when!x=8
Two Rates That Are Related(1-7) In exercises 1-2, assume that x and y are both differentiable functions of t and find the required dy /dt and dx /dt. Equation Find Given 1. dx /dt = 10 y = x (a) dy /dt
AP Physics B Summer Homework (Show work)
#1 NAME: AP Physics B Summer Homework (Show work) #2 Fill in the radian conversion of each angle and the trigonometric value at each angle on the chart. Degree 0 o 30 o 45 o 60 o 90 o 180 o 270 o 360 o
Put in simplest radical form. (No decimals)
Put in simplest radical form. (No decimals) 1. 2. 3. 4. 5. 6. 5 7. 4 8. 6 9. 5 10. 9 11. -3 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 3 28. 1 Geometry Chapter 8 - Right Triangles
Besides the reported poor performance of the candidates there were a number of mistakes observed on the assessment tool itself outlined as follows:
MATHEMATICS (309/1) REPORT The 2013 Mathematics (309/1) paper was of average standard. The paper covered a wide range of the syllabus. It was neither gender bias nor culture bias. It did not have language
Module 13 Trigonometry (Today you need your notes)
Module 13 Trigonometry (Today you need your notes) Question to ponder: If you are flying a kite, you know the length of the string, and you know the angle that the string is making with the ground, can
Chapter 10. Right Triangles
Chapter 10 Right Triangles If we looked at enough right triangles and experimented a little, we might eventually begin to notice some relationships developing. For instance, if I were to construct squares
Right is Special 1: Triangles on a Grid
Each student in your group should have a different equilateral triangle. Complete the following steps: Using the centimeter grid paper, determine the length of the side of the triangle. Write the measure
Areas of Parallelograms and Triangles 7-1
Areas of Parallelograms and Triangles 7-1 Parallelogram A parallelogram is a quadrilateral where the opposite sides are congruent and parallel. A rectangle is a type of parallelogram, but we often see
Name: Class: Date: Geometry Chapter 4 Test Review
Name: Class: Date: ID: C Geometry Chapter 4 Test Review. 1. Determine the measure of angle UPM in the following figure. Explain your reasoning and show all your work. 3. Determine the side length of each
Week 11, Lesson 1 1. Warm Up 2. Notes Sine, Cosine, Tangent 3. ICA Triangles
Week 11, Lesson 1 1. Warm Up 2. Notes Sine, Cosine, Tangent 3. ICA Triangles HOW CAN WE FIND THE SIDE LENGTHS OF RIGHT TRIANGLES? Essential Question Essential Question Essential Question Essential Question
Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up
Solve applied problems using the attributes of similar triangles. Solve problems using ratio and proportions. Investigate the fundamental concepts behind trigonometry: three basic trig functions and how
Unit 7 Trigonometry Test #1 Review
Secondary Math 3 Name x 2^0Y1T9l NKYu]tga\ gsgovfztywdamr]e _LYLrg.n j HDlRls TrgiUgMhntvsZ TryedsUearbverdz. Unit 7 Trigonometry Test #1 Review Find the value of the trig function indicated. Date Period
Date Lesson Assignment Did it grade Friday Feb.24
PAP Pre-Calculus Lesson Plans Unit Sem 2 3 rd term Johnston (C4) and Noonan (C6) February 24 th to March 9 th 202 - Vectors Date Lesson Assignment Did it grade Friday Feb.24 Law of Sines/Cosines, Area
84 Geometric Mean (PAAP and HLLP)
84 Geometric Mean (PAAP and HLLP) Recall from chapter 7 when we introduced the Geometric Mean of two numbers. Ex 1: Find the geometric mean of 8 and 96.ÿ,. dÿ,... : J In a right triangle, an altitude darn
Math-3. Lesson 6-5 The Law of Sines The Ambiguous Case
Math-3 Lesson 6-5 The Law of Sines The miguous Case Quiz 6-4: 1. Find the measure of angle θ. Ө = 33.7 2. What is the cosecant ratio for ϴ? Csc Ө = 2 5 5 3. standard position angle passes through the point
I can add vectors together. IMPORTANT VOCABULARY
Pre-AP Geometry Chapter 9 Test Review Standards/Goals: G.SRT.7./ H.1.b.: I can find the sine, cosine and tangent ratios of acute angles given the side lengths of right triangles. G.SRT.8/ H.1.c.: I can
CK-12 Geometry: Special Right Triangles
CK-12 Geometry: Special Right Triangles Learning Objectives Identify and use the ratios involved with isosceles right triangles. Identify and use the ratios involved with 30-60-90 triangles. Review Queue
5-8 Applying Special Right Triangles
5-8 Applying Special Right Triangles Warm Up Lesson Presentation Lesson Quiz Geometry Warm Up For Exercises 1 and 2, find the value of x. Give your answer in simplest radical form. 1. 2. Simplify each
Student Outcomes. Lesson Notes. Classwork. Discussion (20 minutes)
Student Outcomes Students explain a proof of the converse of the Pythagorean Theorem. Students apply the theorem and its converse to solve problems. Lesson Notes Students had their first experience with
Law Of Sines And Cosines Kuta
Cosines Kuta Free PDF ebook Download: Cosines Kuta Download or Read Online ebook law of sines and cosines kuta in PDF Format From The Best User Guide Database Solve application problems using the Law of
1. A right triangle has legs of 8 centimeters and 13 centimeters. Solve the triangle completely.
9.7 Warmup 1. A right triangle has legs of 8 centimeters and 13 centimeters. Solve the triangle completely. 2. A right triangle has a leg length of 7 in. and a hypotenuse length of 14 in. Solve the triangle
OVERVIEW Similarity Leads to Trigonometry G.SRT.6
OVERVIEW Similarity Leads to Trigonometry G.SRT.6 G.SRT.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric
Assignment. Get Radical or (Be) 2! Radicals and the Pythagorean Theorem. Simplify the radical expression. 45x 3 y 7. 28x x 2 x 2 x 2x 2 7x
Assignment Assignment for Lesson.1 Name Date Get Radical or (Be)! Radicals and the Pythagorean Theorem Simplify the radical expression. 1. 60. 60 4 15 15. 8x 5 4. 8x 5 4 7 x x x x 7x 108 108 6 6 45x y
Two Special Right Triangles
Page 1 of 7 L E S S O N 9.3 In an isosceles triangle, the sum of the square roots of the two equal sides is equal to the square root of the third side. Two Special Right Triangles In this lesson you will
Review on Right Triangles
Review on Right Triangles Identify a Right Triangle Example 1. Is each triangle a right triangle? Explain. a) a triangle has side lengths b) a triangle has side lengths of 9 cm, 12 cm, and 15 cm of 5 cm,7
Gary Delia AMS151 Fall 2009 Homework Set 3 due 10/07/2010 at 11:59pm EDT
Gary Delia AMS151 Fall 2009 Homework Set 3 due 10/07/2010 at 11:59pm EDT 1. (2 pts) The angle of elevation to the top of a building is found to be 9 from the ground at a distance of 6000 feet from the
Math 20-3 Admission Exam Study Guide Notes about the admission exam:
Math 20-3 Admission Exam Study Guide Notes about the admission exam: To write the exam, no appointment is necessary; drop-in to MC221 (Testing) and ask for the 20-3 exam. You ll be given a form to take
A life not lived for others is not a life worth living. Albert Einstein
life not lived for others is not a life worth living. lbert Einstein Sides adjacent to the right angle are legs Side opposite (across) from the right angle is the hypotenuse. Hypotenuse Leg cute ngles
Trig Functions Learning Outcomes. Solve problems about trig functions in right-angled triangles. Solve problems using Pythagoras theorem.
1 Trig Functions Learning Outcomes Solve problems about trig functions in right-angled triangles. Solve problems using Pythagoras theorem. Opposite Adjacent 2 Use Trig Functions (Right-Angled Triangles)
Unit 2: Right Triangle Trigonometry RIGHT TRIANGLE RELATIONSHIPS
Unit 2: Right Triangle Trigonometry This unit investigates the properties of right triangles. The trigonometric ratios sine, cosine, and tangent along with the Pythagorean Theorem are used to solve right
Section 8: Right Triangles
The following Mathematics Florida Standards will be covered in this section: MAFS.912.G-CO.2.8 Explain how the criteria for triangle congruence (ASA, SAS, SSS, and Hypotenuse-Leg) follow from the definition
Chapter 8: Right Triangles (page 284)
hapter 8: Right Triangles (page 284) 8-1: Similarity in Right Triangles (page 285) If a, b, and x are positive numbers and a : x = x : b, then x is the between a and b. Notice that x is both in the proportion.
Trig Functions Learning Outcomes. Solve problems about trig functions in right-angled triangles. Solve problems using Pythagoras theorem.
1 Trig Functions Learning Outcomes Solve problems about trig functions in right-angled triangles. Solve problems using Pythagoras theorem. Opposite Adjacent 2 Use Trig Functions (Right-Angled Triangles)
MATHEMATICS: PAPER II
CLUSTER PAPER 2016 MATHEMATICS: PAPER II Time: 3 hours 150 marks PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY 1. This question paper consists of 28 pages and an Information Sheet of 2 pages(i-ii).
Sin, Cos, and Tan Revealed
Sin, Cos, and Tan Revealed Reference Did you ever wonder what those keys on your calculator that say sin, cos, and tan are all about? Well, here s where you find out. You ve seen that whenever two right
BND TechSource. Chain & Sprocket Simulation using CATIA V5 DMU Kinematics. (Revised 27SEP09)
Chain & Sprocket Simulation using CATIA V5 DMU Kinematics (Revised 27SEP09) Website = http://bndtechsource.ucoz.com The following licenses are required to simulate Chain & Sprocket movement with CATIA
Skills Practice Skills Practice for Lesson 3.1
Skills Practice Skills Practice for Lesson.1 Name Date Get Radical or (Be) 2! Radicals and the Pythagorean Theorem Vocabulary Write the term that best completes each statement. 1. An expression that includes
1 What is Trigonometry? Finding a side Finding a side (harder) Finding an angle Opposite Hypotenuse.
Trigonometry (9) Contents 1 What is Trigonometry? 1 1.1 Finding a side................................... 2 1.2 Finding a side (harder).............................. 2 1.3 Finding an angle.................................
Name: Date: Period: Score: Rotational Symmetry
Rotational Symmetry Symmetry: Symmetry is the property of a shape that allows it to be carried onto itself either by by reflection, or rotation. The second kind of symmetry is called rotational symmetry.
Agood tennis player knows instinctively how hard to hit a ball and at what angle to get the ball over the. Ball Trajectories
42 Ball Trajectories Factors Influencing the Flight of the Ball Nathalie Tauziat, France By Rod Cross Introduction Agood tennis player knows instinctively how hard to hit a ball and at what angle to get
Chapter. Similar Triangles. Copyright Cengage Learning. All rights reserved.
Chapter 5 Similar Triangles Copyright Cengage Learning. All rights reserved. 5.4 The Pythagorean Theorem Copyright Cengage Learning. All rights reserved. The Pythagorean Theorem The following theorem will
Year 10 Mathematics, 2009
Student s Name: Teacher s Name: 10 Year 10 Mathematics, 2009 Algebra Use straightforward algebraic methods and sketch and interpret features of linear graphs Time: 20 minutes. Check that you have entered
SQUARE ROOTS. Pythagoras theorem has been a perennially interesting. Drawing A SPIRAL OF. ClassRoom
Drawing A SPIRAL OF SQUARE ROOTS ClassRoom KHUSHBOO AWASTHI "Mathematics possesses a beauty cold and austere, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show."
Area And The Law Of Sines Tesccc
Area And The Tesccc Free PDF ebook Download: Area And The Tesccc Download or Read Online ebook area and the law of sines tesccc in PDF Format From The Best User Guide Database Holt Algebra 2. 13-5 The
MORE TRIGONOMETRY
MORE TRIGONOMETRY 5.1.1 5.1.3 We net introduce two more trigonometric ratios: sine and cosine. Both of them are used with acute angles of right triangles, just as the tangent ratio is. Using the diagram
A Low Cost Digital Angle Gage, version 3
A Low Cost Digital Angle Gage, version 3 By R. G. Sparber Copyleft protects this document. 1 Sometimes re-inventing the wheel has advantages. What you see here is just a variation on a sine bar. The accuracy
Write these equations in your notes if they re not already there. You will want them for Exam 1 & the Final.
Tuesday January 30 Assignment 3: Due Friday, 11:59pm.like every Friday Pre-Class Assignment: 15min before class like every class Office Hours: Wed. 10-11am, 204 EAL Help Room: Wed. & Thurs. 6-9pm, here
Parking Lot HW? Joke of the Day: What do you call a leg that is perpendicular to a foot? Goals:
Parking Lot Joke of the Day: HW? What do you call a leg that is perpendicular to a foot? a right ankle Goals: Agenda 1 19 hw? Course Recommendations Simplify Radicals skill practice L8 2 Special Right
Student Instruction Sheet: Unit 4, Lesson 4. Solving Problems Using Trigonometric Ratios and the Pythagorean Theorem
Student Instruction Sheet: Unit 4, Lesson 4 Suggested Time: 75 minutes Solving Problems Using Trigonometric Ratios and the Pythagorean Theorem What s important in this lesson: In this lesson, you will
Title: Direction and Displacement
Title: Direction and Displacement Subject: Mathematics Grade Level: 10 th 12 th Rational or Purpose: This activity will explore students knowledge on directionality and displacement. With the use angle
Law Of Sines Ambiguous Case Worksheet 7 2
Case Worksheet 7 2 Free PDF ebook Download: Case Worksheet 7 2 Download or Read Online ebook law of sines ambiguous case worksheet 7 2 in PDF Format From The Best User Guide Database Worksheet by Kuta
Edexcel GCSE. Mathematics A 1387 Paper 5523/03. November Mark Scheme. Mathematics A 1387
Edexcel GCSE Mathematics A 187 Paper 552/0 November 2007 Mark Scheme Edexcel GCSE Mathematics A 187 NOTES ON MARKING PRINCIPLES 1 Types of mark M marks: method marks A marks: accuracy marks B marks: unconditional
Bishop Kelley High School Summer Math Program Course: Trigonometry and Trigonometry with Pre-Calculus
015 01 Summer Math Program Course: Trigonometr and Trigonometr with Pre-Calculus NAME: DIRECTIONS: Show all work on loose-leaf paper, which ou will turn in with the packet. (NO WORK IN PACKET!) Put final
Lesson 5. Section 2.2: Trigonometric Functions of an Acute Angle 1 = 1
Lesson 5 Diana Pell March 6, 2014 Section 2.2: Trigonometric Functions of an Acute Angle 1 = 1 360 We can divide 1 into 60 equal parts, where each part is called 1 minute, denoted 1 (so that 1 minute is
Functions - Trigonometry
10. Functions - Trigonometry There are si special functions that describe the relationship between the sides of a right triangle and the angles of the triangle. We will discuss three of the functions here.
COMPLEX NUMBERS. Powers of j. Consider the quadratic equation; It has no solutions in the real number system since. j 1 ie. j 2 1
COMPLEX NUMBERS Consider the quadratic equation; x 0 It has no solutions in the real number system since x or x j j ie. j Similarly x 6 0 gives x 6 or x 6 j Powers of j j j j j. j j j j.j jj j j 5 j j
Math 4. Unit 1: Conic Sections Lesson 1.1: What Is a Conic Section?
Unit 1: Conic Sections Lesson 1.1: What Is a Conic Section? 1.1.1: Study - What is a Conic Section? Duration: 50 min 1.1.2: Quiz - What is a Conic Section? Duration: 25 min / 18 Lesson 1.2: Geometry of
25. [Perimeter] 4 2 = Measure each side length of the shape. Add together the side lengths.
![25. [Perimeter] 4 2 = Measure each side length of the shape. Add together the side lengths.](/thumbs/79/79674171.jpg "25. [Perimeter] 4 2 = Measure each side length of the shape. Add together the side lengths.")
25. [Perimeter] Skill 25.1 Finding the perimeter of polygons by measuring their side lengths. Measure each side length of the shape. Q. Use a ruler to find the perimeter of the scalene triangle in millimetres.
Applications of trigonometry
Applications of trigonometry This worksheet and all related files are licensed under the Creative Commons Attribution License, version 1.0. To view a copy of this license, visit http://creativecommons.org/licenses/by/1.0/,
Unit 7. Math Problem 1. This segment will go through the endpoint of the original line segment, perpendicular to the line segment.
Math 1007 Unit 7 1 Construct a square with sides equal to r. 1: Extend the segment and draw a circle centered at one of the endpoints of the segment 2: Draw two larger congruent circles centered where
Chp. 3_4 Trigonometry.notebook. October 01, Warm Up. Pythagorean Triples. Verifying a Pythagorean Triple... Pythagorean Theorem
Chp. 3_4 Trigonometry.noteook Wrm Up Determine the mesure of the vrile in ech of the following digrms: x + 2 x x 5 x + 3 Pythgoren Theorem - is fundmentl reltionship mongst the sides on RIGHT tringle.
DIRECTIONS FOR GEOMETRY CONSTRUCTION PROJECT
Name Period DIRECTIONS FOR GEOMETRY CONSTRUCTION PROJECT Materials needed: Objective: Standards: 8 pieces of unlined white computer paper (8.5 in. by 11in.), compass, ruler, protractor, pencil, and markers/colored
Geometry Chapter 7 Review Right Triangles Use this review to help prepare for the Chapter 7 Test. The answers are attached at the end of the document.
Use this review to help prepare for the hapter 7 Test. The answers are attached at the end of the document. 1. Solve for a and b. 2. Find a, b, and h. 26 24 a h b 10 b a 4 12. The tangent of is. 4. A is
2011 Canadian Intermediate Mathematics Contest
The CENTRE for EDUCATION in MATHEMATICS and COMPUTING www.cemc.uwaterloo.ca 011 Canadian Intermediate Mathematics Contest Tuesday, November, 011 (in North America and South America) Wednesday, November
Math 15 Test 3 Review Section Change 4.5 yards to inches. Round your answer to the nearest inch. (1 yd = 3 ft, 1 ft = 12 in)
Page 1 Math 15 Section 6.3 18. Change 4.5 yards to inches. Round your answer to the nearest inch. (1 yd = 3 ft, 1 ft = 12 in) 30. Change 528 inches to feet. (1 ft = 12 in) 42. Change 3 1/16 pounds to ounces.
Trigonometry. terminal ray
terminal ray y Trigonometry Trigonometry is the study of triangles the relationship etween their sides and angles. Oddly enough our study of triangles egins with a irle. r 1 θ osθ P(x,y) s rθ sinθ x initial
Discovering Special Triangles Learning Task
The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still
Energy Drilling Prospects
01 05 Energy Drilling Prospects Fraser Offshore Ltd is a drilling project management company. It designs, plans and drills oil wells for clients who are typically oil & gas companies or large utilities
Cumulative Test. Name. Score. Show all work on this paper. Please use the Student Reference Guide.
Name Score Math Course 1 1B 1. Use the numbers 5, 11, and 16 to make two addition facts and two subtraction facts. 11 + 12 12 + 12 12 12 12 12 2. Use the numbers 4, 16, and 64 to make two multiplication