Trig Graphing Openers

We returned from spring break yesterday with me being fresh off from the NCTM Boston conference.  I went through the links people added online and got even more ideas.

I put some of these together to open our first class back to Trig Graphing.  Before vacation, the kids were introduced to graphing all 6 trig functions.  They are pretty good with sin and cos, need to learn what the A does in tangent and cotangent, and need more practice with sec and cos. 

They were already taught all the vocabulary too.  So, let's jog those memories and get them thinking. 

I started with this Which One Doesn't Belong and Why.  Check out the link here: WODB  I got the chance to meet the author of the book Christopher Danielson while at NCTM and working the MTBoS booth.  Teachers are collaborating to make the website fill up with ideas.

Then, I found the multiple choice questions on one of the presentations:

And, next was the most fun.  It was partner graphing exercise found in a presentation.  Here is what I told them.  They had some discussion who would graph first.  They were unsure which might be the lesser evil.

And, this was the first equation:

They struggled a bit getting used to trying to put it in words and it took a little while but overall, they did well. 

I had one student explain to me how to draw it while I was at the board.  It was impressive.  He told me to draw the x and y axis.  Then, draw a dotted midline at y=3.  Draw a max line at y=5. Draw a min line at y=1.  Then, he told me to write the x values in increments of pi/2.  Then, he just told me to plot points.  Plot (pi/2, 5) etc.  I asked him if he had done it that well with his partner and the partner shook his head no.  

So, then it was time to switch and the groans came....

We weren't too familiar with cotangent.  They were thinking more of the tangent parent and transforming the point (0,0).  Oops.  But, they got close.  They didn't know what the 2 might do.  They knew in sin and cos it would change the amplitude to 2 but what does it do here?  Ah, that lead us into our next activity on graphing tan and cot and figuring out what that A value does.  They saw a need for it!

These were just our openers but they were a really great welcome back from vacation.  I enjoyed them.  They were some great discussions.