Precal Blog

In addition to the Curtis Method and the Ranta Conjecture we had a couple of really good questions come up. One in particular deserves some more attention.

We were trying to graph `y=-4+5sin((2*pi)/3(x+1))`

The first attempt was to try and avoid radians and graph `y=-4+5sin(120(x+1))`. Then the question was asked – “If we are converting `(2*pi)/3` to degrees, then doesn’t the 1 (radian) have to be converted also? So, going with that idea we have: `y=-4+5sin(120(x+57.295…))` or exactly: `y=-4+5sin(120(x+180/pi)` That seemed very reasonable. Before we had time to discuss it any further time ran out.

Looking at a table of values though, it is clear that the two equations above are not equivalent. Why not? After all `(2*pi)/3` radians is equal to 120 degrees, and 1 radian is equal to `180/pi` degrees.

I won’t tell you the answer (I know that surprises you) but I will give you the two equations that are equivalent and you can think about why these two are but the orignal two are not.

`y=-4+5sin((2*pi)/3(x+1))` in radians is equivalent to `y=-4+5sin((2*pi)/3(x+180/pi))` in degrees.

What’s going on?

Things look like they are going well – although I am certain there is too much talking and not enough thinking going on. Try to tighten things up – we have a lot to do in our last quarter together.

By the way – Mr. Byrne would be the spelling you want. Thanks to everyone for being flexible. See you Friday.

(Jon and Blair are the last two scribes for this cycle and then we start over.)

I don’t know about everyone else, but i plan on study hardcore for this test on Wed. How can you pass up a trip to Spain….for a math test?!?

Am I the only one who thinks the new blog looks super cooler than the old one? I enjoy that i can login near the top of the screen now instead of scrolling all the way down too. Nice job Mr. Bieniek.

Hi folks. Sorry about the delay in getting organized for second semester. The scribe list is now completely up to date. 4th hour needs a scribe for Friday’s class. Someone please step up and do it.

Also remember that when you comment, you are shooting for comments that enhance – not judge. Please read this post if you aren’t sure what I mean.

One last thing. If you Google precalculus blog we are the 11th site listed. That is pretty good. If you use Yahoo our blog is the first site listed! What that means is that the content on our blog matches very closely with what we say our blog is about. After only a semesters worth of work I would say that is pretty impressive. Nice work!

After we looked at the last example today I realized I should have been more clear about the restrictions on the composition problems we looked at.

For the problems we looked at, like `sin(tan^-1(x))`, you need to make sure that `x` is in the domain of `tan^-1(x)`. But once you do that, then really the only question is – are any of those values not allowed in `sin(x)`? For this example since inverse tangent accepts all real numbers and sine can evaluate all real numbers, we have no restriction, and `x in RR`.

My statement that `x` has to be in the domain of the inside function and in the range of the outside function helps us to avoid mistakes like `cos^-1(cos(10))=10`. This is not true although very tempting. In order for this to be true, 10 would have to be in the range of `cos^-1(x)`, which it isn’t. The range of `cos^-1(x)` is `[0,pi]`.

I hope you all really enjoy your time off – you have certainly earned it. If you post or comment during break you may not see it show up right away. Don’t worry – it will. Don’t post or comment twice, just be patient. -Peace

I enjoyed reviewing the photographs you took for this assignment. If you can e-mail me the digital pics I’d like to put up a slide show on the blog so everyone can see your work. In fact Flickr has a neat tool which lets you annotate your photograph with click-able boxes that could, for example, reveal information about your sinusoid or its equation.

I thought Blair submitted a noteworthy entry. His friend has a snake that has been photographed by National Geographic. Cool!! You can see it here.

What mathematical theorem is represented by the following mosaic? Justify your answer.

Please take a look at the graph we made for #3.
We determined that the period was `pi` but when we graphed it I don’t think we actually had a period of `pi`. The final graph should look like this:

agraph
xmin=-3pi; xmax=3pi; xscl=pi/2; ymin=-5; ymax=20; yscl=5; axes();
plot(10+5sin(2x+pi));
endagraph

The graph uses 1.6 as an approximation of `pi/2`.