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"