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"

Cool Math Stuff

A cool thing to watch...
Vi Hart's work is amazing, and I bet she would approve of the word "mathmagical!"  Check out this great video that applies to our trig graphs.  What do you think...is pi wrong?  Should we use Tau?


I could spend hours watching all of her videos, but I know you'll love her Doodling in Math Class series.  Check 'em out!

A cool series to read...
A modern math superhero and professor, Steven Strogatz, wrote an incredible series a couple years ago called "The Elements of Math."  He includes a clip from Sesame Street, compares logarithms to power tools, and had the best titles for each post.  Each one of those articles brought my day to at least an 8! :-)

He just started another series, and the first article, Singular Sensations, was published this week.  I'm looking forward to reading the rest of his essays!

Do you know any other cool math videos, facts, trivia, posts, or links?

I Have Learned...

After two weeks of school, what have you learned so far?  Thinking specifically about our math class, what have you learned about how our class works, how to prepare for the class, how to complete homework, and how to prepare for a test?  What can you do differently this week?  How will you prepare for our next test?

Don't panic if your grade is not what you want at this point.  It's OK to make mistakes!  Learn from your mistakes!  Make new mistakes. :)  Do you have any favorite "failure quotes?"

“Success is not final, failure is not fatal: 

it is the courage to continue that counts.” 

~Winston Churchill

"If you fell down yesterday,

stand up today."

~H.G. Wells

Math Is...

I loved reading all of your Mathographies!  I will re-read them at the end of the six-weeks, at the beginning of the 2nd semester, and probably several other times throughout the year.  Thank you for all of your responses!  I'm looking forward to a great year with you all as my students.

Here's a wordle of your "Math Is..." responses.  Some of you created great similes and metaphors, by the way. :)

By the way, in our two classes, I think we have student representatives from every organization and sport.  I think you were about split 50-50 between which you enjoyed more: algebra and geometry.  (I'm more of an algebra person, myself.)  I loved seeing this comment in numerous papers: "Math is like a puzzle!"  I agree!

YES, I offer LOTS of tutoring, but you sometimes have to specifically get on my calendar...but I WILL find time for you.  And YES, I do offer some extra credit, but I'm still trying to work on my details and changing my philosophy about that.

I know we're going to have a wonderful year learning from each other!  I'm so glad you're in my math class!