Test Time!

OK, it's time for our next test, so what changes do you need to make to be ready for test #2?  What do you do to prepare for a math test?  Can you think of anything that I might do to make the questions more interesting?  

Here is a cool graphing applet to show transformations of sine and cosine graphs.  (You will have to allow Java for this applet to run, and click on the links on the left side of the screen.)

I have a growth mindset about making videos to help you, so here's attempt #2.  (I also got a bit of advice from my friend Mr. Gonzales who suggested a "Crash Course" type video.)


And here's a lower production video for a quick review of even and odd functions.  (It worked at home, but now it says "converting," so I hope you'll be able to view this video!!  Sigh.)

Are these review videos helpful at all?  Please let me know!  

What improvements or other suggestions do you have?  

I'm still learning!

Graphs of Sine and Cosine

For my first absence of the year (several of your teachers will be attending this training) I tried to create a video version of our notes.

I must admit, the video is pretty terrible, but the instruction is adequate. :)  You can hear my pen tap on the screen, I used a couple words wrong (function rather than transformation; stretch rather than shift) I am sometimes too quiet and sometimes too loud, and I think at one point, you hear my cat purring in the back ground! BUT, I have a growth mindset about preparing these types of lessons for you, so I won't give up after my first fail.  And I didn't want to learn how to edit because this has already taken me 3 hours to create!

So please enjoy my version of sine and cosine graphs.  The notes for this section are here, but I'll have copies for you in class.

If you don't completely understand everything, have patience (and a growth mindset).  A classmate may help you and/or I know you can find countless other resources online to help with the topic.  I'll return on Wednesday, and we'll continue the discussion about trig graphs, but we'll have even more transformation fun in store.

Once you finish the video, please complete the quick survey about 

your learning and understanding.

If you have any additional suggestions, concerns, or questions, please feel free to leave them in the comments!  Thanks, and have a wonderful day.

Not Quite the North Pole, but Almost as Fun!

When I first mentioned polar coordinates, did you immediately think "North Pole!" and then "Santa?"  (I know that's the way my mind works every time I think about polar graphs, especially at this time of year!) 

(And since we're talking North Pole, I'll share some KLas family trivia... I've told you that my sister lived in Alaska for a long time, and her wedding was almost exactly 8 years ago...happy anniversary Allison & Steve!  So when our entire family ventured to Alaska for her wedding during Thanksgiving, 2004, we had to go to North Pole, Alaska, shop at the Santa Clause house, and take a picture of the real north pole!)

That's my dad with me...& yes, there are geocaches close by!

Is that Rudolph, peeking around the corner?

Visiting the North Pole is oh-so-much fun, but look at the possible graphs you can make...doesn't that look like fantastic fun, too?! ;)  And you you will be able to create these graphs by the end of the week...no winter visits to Alaska required!

Great use for cardioid graphs!

Since our study of polar graphs and coordinates will be abbreviated, I wanted to provide a few resources for you to help with your studies, so here you go:

Written resources:

• Great examples from a professor at Lamar College
• Another math teacher's resources for students
• From the appropriately named "Math is Fun" website - examples of converting between coordinates
• How to create a polar graph using a table
• Using your calculator to create polar graphs
• An explanation and examples of all of the different polar graphs
• Free graph paper to download

Video/Interactive Resources (most require Java):

• Video tutorial of basics of polar coordinates and graphs
• Great interactive site to explain polar
• Interactive sites to create polar graphs (like our "web assignment") - found here and here and here

If you find another resource that might help a classmate, please list it in the comments below.  If you create a cool polar graph, take a screen shot and email it to me, and I'll post it here!

Aren't polar graphs cool?

Sinusoidal Functions as Math Models HELP

OK, I know you can do these problems, but it definitely takes some practice!  I've watched several videos and found a few links to help you.  I also created a tiny "video" using the Educreations app.  You should be able to watch my videos just fine from your computer, but if you're on an iPad, you have to download the free app.  Unfortunately, this video does not work on an iPhone. :-(

• My video on solving a sinusoidal equation algebraically involving a cosine.
• When is Fiona an ogre vs. a princess?  Use this video to find out!
• Here's an explanation of a water wheel problem.  Thanks, emathguy!
• This PDF shows several problems worked completely.  The problems are even some of the same ones I've assigned, and at a quick glance, they look good, but I haven't checked all of the work.
• One more PDF of some similar problems worked.  I like this one because it shows a few distinct steps (looking for a max/min point, writing an equation as a sine or cosine, etc.) But again, I didn't work through all of the problems for correctness, so use at your own risk! :-)
• The answers to the "Practice Test" are the photos below, and all steps are shown for the algebraic equations:

The answers to your two practice worksheets are posted on EdLine.

Most of these problems (and the ones from the video) were taken from the green trig book (Foerster) section 2.12.  The odd answers are in the back of the book, of course!

If you find any other great hints, please share in the comments below!

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From your comments on your exit ticket: one person asked for problems worked out completely, so I posted those equations above.  Another specific question asked about how do you determine whether your graph is a sin x or cos x (or -sin x or -cos x).

• If the first point you plot is a maximum point, your graph is most likely a cosine because your point is ABOVE the shifted x-axis.

positive cosine--starts at a MAX

• If  the first point you plot is a minimum point, your graph is most likely a negative cosine because your point is ABOVE the shifted x-axis.

negative cosine--1st point is a MIN

• If the first point says something about "the middle" (or the average, equilibrium, at rest, etc.) your graph is most likely a sine graph.  If the object then is pulled down (or something similar) your function is a negative sine.  If the object then moves upward, the function is a positive sine.

negative sine--"middle and down"

positive sine--"middle and up"