Math 20-1

Chapter 2 Trigonometry

Lesson 2.1   Angles in Standard Position

Support Documents

Answer pages

You should be checking your work for EVERY question you do!

To make that easy, you can download the solutions files which have the answers for all the practice problems in the text.

You can print it, though it would be a lot of pages.

I think the best choice would be to keep the files handy, and have them open and ready every time you are working on math.

This saves you the time of flipping to the back of the book every time you need to check an answer.

FOLDER LINK

Formula Page

Math 20-1 is an academic course and you will be expected to memorize a lot of what you are covering in class.

Your teacher will have expectations for the things you will see on a formula page.

The link below is to formula page that you can download and print to use with your course.

You may or may not be allowed to use this on tests, and you may or may not be allowed to ADD your own notes to these pages.

Use of this page depends on your teacher.

What goes on this page is also subjective, so it is subject to change!

Formula Page

Formula page “add ons”

Add on:  This page has a diagram of the two special triangles used for exact values of some trig ratios.
You really should memorize this, but it’s provided here for you to include with your other formula page.
You will need to check with your teacher about whether you can use this on tests  (probably not!)

Focus on...

Lesson Objectives

•	sketching an angle from 0° to 360° in standard position and determining its reference angle

•	determining the quadrant in which an angle in standard position terminates

•	determining the exact values of the sine, cosine, and tangent ratios of a given angle 
	with reference angle 30°, 45°, or 60°

•	solving problems involving trigonometric ratios

Focus on...  Activity

The FOCUS section introduces the main concept that will be covered in the lesson.

TEXT Page 74

Read/Work through the  Focus  section at the top of page 74 in  your textbook.

Do your best to answer the questions given in this section.
These ideas will all be covered in the lesson.

Investigate  Exact Values and Angles in Standard Position

The investigation provides the background for the ideas presented in the lesson.

TEXT Pages 74 - 77

Read/Work through the  Investigate  section on Pages 74 - 77 in your textbook.

A list of materials  you need for the Investigation is given in the side bar.

Your work will be a lot more efficient if you PLAN for and GATHER these items BEFORE you start the Investigation!

You may not have other students to work with.  
No worries!  
If you are working on your own,  answer the questions, AS BEST YOU CAN, before you view the Tutorial that follows.
Once you have done that,  view the video for help with this section.

Informal definition of an angle

In geometry, an angle is formed by two rays with a common endpoint.

Video Tutorial  (INV A)

Part A:	Angles in Standard Position

As a reminder.... do the questions FIRST!   
This is supposed to be an investigation!

Video Tutorial Questions  1 - 3  (INV B)

Reflect and Respond

Video Tutorial Questions 4 - 5  INV C

Definitions  Reflect and Respond 4

Math Open Reference

💡  Definition:	The standard position of an angle occurs when we place its vertex at the origin of a coordinate system and its initial side  (initial arm)  on the positive x axis.

The terminal arm of the angle can end up anywhere....

Some vocabulary.

•	Angle in standard position (directed angle or rotation angle)
•	Vertex
•	Initial arm
•	Terminal arm
•	Clockwise rotation   (negative)
•	Counter-clockwise rotation (positive)
•	Complete rotation (revolution)

Demonstration Angles in Standard Position

Part B: Create a 30°-60°-90° Triangle

Video Tutorial Questions 6 - 7

It’s amazing that with careful folding you can create an equilateral triangle.
I went through the steps given in Questions 6 - 7, and I encourage you to try that!
But..... really, for the purpose of the investigation,  you can use your protractor and simply DRAW an equilateral triangle to use for the next questions.

Video Tutorial Questions 8 - 9    INV D

Video Tutorial Questions 10 - 12   INV E

Reflect and Respond

Video Tutorial Question 13  INV Z

Video Tutorial Question 14  INV F

Video Tutorial Question 15  INV H

Question 16

I hope you tried this first!
One possible method,  fold corner A over to point C, then cut rectangle EBCF off.
Then all you have left is triangle BCD  which is a 45° - 45° - 90° triangle.
Then do the analysis for the trig values

Video Tutorial Question 16  INV W

Link the Ideas

Link the Ideas summarizes the math in the lesson.
A presentation of ideas connected to the lesson focus.

TEXT Pages 77 - 79

Read/Work through the  Link the Ideas  section on Pages 77 - 79 in your textbook.

Except for the section on reference angles,  all this material was covered in the Investigation.

See below for a video on reference angles, AND a demonstration that will let you actively explore the idea.

Demonstration Reference Angles

Watch

Video Tutorial  (REFANG)

Demonstration

Examples

Examples will give you TOOLS for solving problems, and also show you that there may be different ways to approach a question.

Example 1  Sketch an Angle in Standard Position,   0° ≤ θ < 360°

TEXT Pages 79 - 80

Work through Example 1 on Pages 79 - 80 in your textbook.

Watch

I didn’t do a video here,  I think the diagrams in the text are clear.

Your Turn

YOUR TURN gives YOU the chance to try to do a problem ON YOUR OWN,  using the example as  a model.

Use the Video Tutorial for help, or to check your work, BUT... you should do your best to do this question ON YOUR OWN FIRST!

Video Tutorial

Example 2  Determine a Reference Angle

TEXT Page 80

Work through Example 2 on Page 80  in your textbook.

Watch

Video Tutorial

Your Turn

YOUR TURN gives YOU the chance to try to do a problem ON YOUR OWN,  using the example as  a model.

Use the Video Tutorial for help, or to check your work, BUT... you should do your best to do this question ON YOUR OWN FIRST!

Video Tutorial

Example 3  Determine the Angle in Standard Position

TEXT Page 81

Work through Example 3 on Page 81 in your textbook.

Watch

Video Tutorial

Your Turn

YOUR TURN gives YOU the chance to try to do a problem ON YOUR OWN,  using the example as  a model.

Use the Video Tutorial for help, or to check your work, BUT... you should do your best to do this question ON YOUR OWN FIRST!

Video Tutorial

Example 4  Find an Exact Distance

TEXT Page 82

Work through Example 4 on Page 82 in your textbook.

Watch

Video Tutorial

Your Turn

YOUR TURN gives YOU the chance to try to do a problem ON YOUR OWN,  using the example as  a model.

Use the Video Tutorial for help, or to check your work, BUT... you should do your best to do this question ON YOUR OWN FIRST!

Video Tutorial

Key Ideas

Key Ideas summarizes the main new concepts of the lesson.

•	Carefully read through each of the bullet points in this section.

•	If you are unclear about any of these ideas,  ASK YOUR TEACHER FOR HELP!

Check Your Understanding    (Practice Problems)

Doing Practice Problems

Practice problems reinforce the math presented in this lesson.

•	Work through the practice problems for this lesson.
	These problems are for practice, you don’t need to hand them in!
	(your teacher may assign specific questions for you to complete)

•	Use the answers in the back of the book to CHECK YOUR WORK!

•	If you make a mistake, TRY TO FIX IT!

•	If you need help or want more information, view the video solutions provided.

•	If you still need more help,  CONTACT YOUR TEACHER!

NOTE!
There are MANY practice questions.
In the interests of time,  I will be selectively skipping some of them.
You have access to the solutions, and you can use those for help as needed.
If the presentation seems straight-forward, I won’t create a video.
I’m hoping that as this course continues to be developed, that if MORE HELP is needed for a specific question,  the missing videos can be added at a later date.

Types of Practice Problems

Practice 
These questions allow you to check your understanding of the concepts. 
You can often do the first few questions by checking the Link the Ideas notes or by following one of the worked Examples.

Apply 
These questions ask you to apply what you have learned to solve problems. 
You can choose your own methods of solving a variety of problem types.

Extend 
These questions may be more challenging. 
Many connect to other concepts or lessons. 
They also allow you to choose your own methods of solving a variety of problem types.

Create Connections
These questions focus your thinking on the Key Ideas and also encourage communication. 
Many of these questions also connect to other subject areas or other topics within mathematics.

Mini Lab
These questions provide hands-on activities that encourage you to further explore the concept you are learning.

Notes

Question 1,    I didn’t do a video for this one.

Question 2,    I didn’t do a video for this one.

Question 3,    I didn’t do a video for this one.

Question 4,    I didn’t do a video for this one.

Question 9,    I didn’t do a video for this one.

Question 11,    I didn’t do a video for this one.

Question 14,    I didn’t do a video for this one.

Question 16,    I didn’t do a video for this one.

Question 18,    I didn’t do a video for this one.

Question 22
Below is the demonstration I used in the video

Question 23,    I didn’t do a video for this one.
A GREAT question, but exploring relationships you will see in much greater detail in a future math course.

Video Solution Links

Check your work for every problem you do!
If you make a mistake,  try to fix it!
Use the video solutions for more information.
If a problem still doesn’t make sense, ASK YOUR TEACHER FOR HELP!

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({{"CC 22",  , "CC 24"}})