Math 20-1

Chapter 2 Trigonometry

Lesson 2.1  Trigonometric Ratios of Any Angle

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!)

Add on:  This page has the “sign rule” for trig ratios of angles in all four quadrants
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!)

Add on:   This page has ALL the exact values for angles between 0 and 360°.   See question 19 from the practice problems.
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!)  (I’d say definitely not...)

Focus on...

Lesson Objectives

•	determining the distance from the origin to a point (x, y) on the terminal arm of an angle

•	determining the value of sin θ, cos θ, or tan θ given any point (x, y) on the terminal arm of angle θ

•	determining the value of sin θ, cos θ, or tan θ for θ = 0°, 90°, 180°, 270° or 360°

•	solving for all values of θ in an equation involving sine, cosine, and tangent

•	solving a problem involving trigonometric ratios

Focus on...  Activity

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

TEXT Page 88

Read/Work through the  Focus  section at the top of page 88 in  your textbook.

Investigate Trigonometric Ratios for Angles Greater Than 90°

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

TEXT Pages 88 - 89

Read/Work through the  Investigate  section on Pages 88 - 89 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.

Investigation

Video Tutorial Questions 1 - 2 INV A

Video Tutorial Questions 3 - 5   INV B

Reflect and Respond

Video Tutorial Questions 6 - 8  INV C

Link the Ideas

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

TEXT Page 90

Read/Work through the  Link the Ideas  section on Page 90 in your textbook.

Demonstration

Video Tutorial  (LINK)

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  Write Trigonometric Ratios for Angles in Any Quadrant

TEXT Page 91

Work through Example 1 on Page 91 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 2  Determine the Exact Value of a Trigonometric Ratio

TEXT Page 91

Work through Example 2 on Page 91  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 Trigonometric Ratios

TEXT Page 92

Work through Example 3 on Page 92 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  Determine Trigonometric Ratios of Quadrantal Angles

TEXT Page 93

Work through Example 4 on Page 93 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 5  Solve for an Angle Given Its Exact Sine, Cosine, or Tangent Value

TEXT Page 94

Work through Example 5 on Page 94 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 6  Solve for an Angle Given Its Approximate Sine, Cosine, or Tangent Value

TEXT Page 95

Work through Example 6 on Page 95 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 6,    I didn’t do a video for this one.

Question 13,    I didn’t do a video for this one.

Question 14,    I didn’t do a video for this one.
A great question,  I’ve mentioned the ideas behind this question several times.
DO this question, check the solutions for help.

Question 17,    I didn’t do a video for this one.

Question 19,    I didn’t do a video for this one.
I’ve included the answer page as an “add on” formula page.
Any student serious about their success in math , especially if you take Math 30 - 1,  should either memorize these values, or know how to quickly generate them.
There are some ways to make this easier, but you’ll see some of those “memory devices” in the next class.
If you are really interested.... do an online search for “unit circle values” and you’ll get LOTS of material to help you.

Question 20,    I didn’t do a video for this one.

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!

({{"Question 1", "Question 2", "Question 3", "Question 4", "Question 5"}, { , "Question 7", "Question 8", "Question 9", "Question 10"}, {"Question 11", "Question 12",  ,  , "Question 15"}, {"Question 16",  , "Question 18",  ,  }, {"Question 21", "Question 22", "Question 23", "Question 24", Question 25}})

Question CC 26,    I didn’t do a video for this one.

Question CC 27,    I didn’t do a video for this one.
blah

Question 30,    I created a very simple animation/interactive for this question.
If I had more time I could make it much more elegant, but if you want to explore this question, it’s a good start.
LINK

({{ ,  , "CC 28", "CC 29", "CC 30"}})