MATH 1201 Learning Guide Unit7 PDF

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MATH 1201 Learning Guide Unit7...

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Learning Guide Unit 7 Site: Course:

University of the People MATH 1201 College Algebra - AY2021T3

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Learning Guide Unit 7

Description Learning Guide Unit 7

Table of contents Overview Introduction Reading Assignment Discussion Assignment Written Assignment Learning Journal Self-Quiz Checklist

Overview

Unit 7: Foundations of Trigonometry

Topics: Angles and the Unit Circle Trigonometric Functions and their Graphs Inverse Trigonometric Functions

Learning Objectives: By the end of this Unit, you will be able to: 1. Recognize the relationship between angles, the unit circle, and trigonometric functions. 2. Construct the graph the trigonometric functions. 3. Use trigonometric identities to verify other trigonometric identities.

Tasks: Read the Learning Guide and Reading Assignments Participate in the Discussion Assignment (post, comment, and rate in the Discussion Forum) Complete and submit the Written Assignment Complete an entry in the Learning Journal Take the Self-Quiz

Introduction

For over a thousand years, trigonometry served as the highest level of mathematics humanity had achieved. The Babylonians in uenced the trigonometry we use today. The Mayans used trigonometry to map the motion of stars with stunning accuracy—the Mayans didn’t know about the wheel, and couldn’t work iron, but still knew trigonometry. Even today, trigonometry is critical to our understanding of astronomy. Phenomena that exhibit periodic patterns are abundant in scienti c theories and in nature, and are the subject of research in science in general and in mathematics itself. Trigonometric functions provide a means by which models can be elaborated to describe such patterns and to predict their behavior as much as possible. Trigonometry is a powerful subject, and no student of mathematics can go far without mastering the concepts.

Reading Assignment

Abramson, J. (2017). Algebra and trigonometry. OpenStax, TX: Rice University. Read the following sections in Chapters 7 and 8: Section 7.1 Angles Section 7.2 Right Triangle Trigonometry Section 7.3 Unit Circle Section 8.1 Graphs of the Sine and Cosine Functions Section 8.2 Graphs of the Other Trigonometric Functions Section 8.3 Inverse Trigonometric Functions You should attempt the exercises in the book as indicated below. These exercises help to establish an understanding of the concepts involved. If necessary, reread the examples and exercises solved in the book. The answers are at the end of the book. Section 7.1 exercises: 1, 11, 25, 31, 35, 43, 47, 51, 55, 65, 71 Section 7.2 exercises: 3, 11, 21, 31, 41, 51, 55 Section 7.3 exercises: 1, 7, 11, 23, 35, 43, 51, 61, 71, 81, 91, 101 Section 8.1 exercises: 1, 11, 21, 31, 43 Section 8.2 exercises: 3, 11, 21, 31, 41, 55 Section 8.3 exercises: 5, 11, 23, 35, 43, 51, 61 You are allowed to use the book and other resources to answer the problems. You are welcome to ask about these in the Course Forum.

Optional Video Resources Access these online resources for additional instruction and practice with trigonometry. Mathispower4u. (2011, May 24). Example: Determine what trig function relates speci c sides of a right triangle [Video le]. Retrieved from

Example: Determine What Trig Functio…

Mathispower4u. (2010, Mar 1). Determine trigonometric function values using the unit circle [Video Fle]. Retrieved from

Determine Trigonometric Function Valu…

Mathispower4u. (2011, May 26). More examples: Determining trig function values using the unit circle [Video le]. Retrieved from

More Examples: Determining Trig Func…

Mathispower4u. (2010, May 11). Graphing sine and cosine with transformations [Video le]. Retrieved from

Graphing Sine and Cosine with Transfo…

Mathispower4u. (2010, May 3). Graphing the tangent function [Video Rle]. Retrieved from

Graphing the Tangent Function

Mathispower4u. (2011, June 3). Examples: Evaluate expression involving inverse trig functions (Part 1) [Video le]. Retrieved from

Examples: Evaluate Expression Involvin…

Discussion Assignment

One of the largest issues in ancient mathematics was accuracy—nobody had calculators that went out ten decimal places, and accuracy generally got worse as the numbers got larger. The famous Eratosthenes experiment, that can be found at https://www.famousscientists.org/eratosthenes/, relied on the fact known to Thales and others that a beam of parallels cut by a transverse straight line determines equal measure for the corresponding angles. Given two similar triangles, one with small measurements that can be accurately determined, and the other with large measurements, but at least one is known with accuracy, can the other two measurements be deduced? Explain and give an example. The similarity of triangles gives rise to trigonometry. How could we understand that the right triangles of trigonometry with a hypotenuse of measure 1 represent all possible right triangles? Ultimately, the similarity of triangles is the basis for proportions between sides of two triangles, and these proportions allow for the calculations of which we are speaking here. The similarity of triangles is the foundation of trigonometry. Your Discussion should be a minimum of 250 words in length and not more than 750 words.

Written Assignment

Complete the following questions utilizing the concepts introduced in this unit. 1. Find the length of an arc in a circle of radius 10 centimeters subtended by the central angle of 50°. Show your work.

2. Graph

on [-4π, 4π] and verbalize how the graph varies from the graphs of .

Graph on the window [−5π, 5π] and describe freely what the graph shows. You can use www.desmos.com/calculator to obtain the graphs.

3. A 23-ft ladder leans against a building so that the angle between the ground and the ladder is 80°. How high does the ladder reach up the side of the building? Show the steps of your reasoning.

Learning Journal

Re ect on the concepts of trigonometry. What concepts (only the names) did you need to accommodate the concepts of trigonometry in your mind? What are the simplest trigonometry concepts you can imagine? In your day to day, is there any occurring fact that can be interpreted as periodic patterns? What strategy are you using to get the graphs of trigonometric functions? The Learning Journal entry should be a minimum of 400 words and not more than 750 words.

Self-Quiz

The Self-Quiz gives you an opportunity to self-assess your knowledge of what you have learned so far.

The results of the Self-Quiz do not count towards your \nal grade, but the quiz is an important part of the University’s learning process and it is expected that you will take it to ensure understanding of the materials presented. Reviewing and analyzing your results will help you perform better on future Graded Quizzes and the Final Exam. Please access the Self-Quiz on the main course homepage; it will be listed inside the Unit.

Checklist

Read the Learning Guide and Reading Assignments

Participate in the Discussion Assignment (post, comment, and rate in the Discussion Forum)

Complete and submit the Written Assignment

Complete an entry in the Learning Journal

Take the Self-Quiz...