Precal Blog

Leave your book on the shelf and access it on the internet! All you need to do is visit the following site and http://www.keymath.com/PreCalc use the ClassPass that I give you. If you want the ClassPass before Monday, send me an e-mail and I will get it to you.

Also, take a look here for the blog or here for the wiki to see where visitors to our sites are located. Nice.

Have a good weekend.

technorati tags:clustrmaps, Precal_blog, Precal_wiki, precalculus

Just a reminder that Becky made a great suggestion to look at problem #44 in section 2-4.  The pattern that the problem points gives you another way to think about those special theta values in the first quadrant.  Once you have those down, reference angles and an understanding of the (u,v) coordinate plane is all you need for any (special) value of theta.

We will soon see another (geometric) method for getting those values down.

technorati tags:trigonometry, precalculus

I’m hoping that everyone gave some thought to the discussion going on towards the end of class today.  I do not expect you to memorize all of those values for sine and cosine.

I expect you to recognize the relationships between angles and their reference angles and then think about where theta terminates in order to determine the exact value.  You might want to commit to memory the first quadrant values for sine and cosine of 30, 45, and 60 degrees.  But even those can be reasoned out by using the right triangles we built in class.  Both triangles (30, 60, 90) and (45,45,90) had a side length of 1.

Is anyone wondering why we are concentrating only on the multiples of 30, 45, and 60?

technorati tags:trigonometry, sine, cosine

It may feel like the end of transformations but it really is only the beginning.  We will now begin to apply our knowledge of transformations as you’ll see in tonight’s work.

Please spend some time mulling over the connectedness of the transformations we looked at.  How are the absolute value transformations we looked at today related to reflections?  How are reflections related to dilations?  How are compositions related to inverse functions?

These are the connections that are going to help you paint the big picture and save you from having to memorize a seemingly disconnected set of “things”.  If you find yourself memorizing more than connecting, you are not making the best use of the material we are covering.

technorati tags:precalculus, transformations, functions

Friday? Ok. Sounds good. Midquarter 1 test this Friday, October 6th. You heard it here first.

(At least some of you did.)

After today’s discussion many of you are going to be tempted to try and boil everything down to some sort of 3 step “procedure” for finding domain of a composite function.

Please do not do that. Do not try and memorize a procedure. This is not Algebra or Geometry – it will not work in the long run. The key is to think hard about what f(g(x)) means and what domain means. Then make the connection between a composite function and its domain. If you cannot make the connection then something is wrong. Either you don’t completely understand domain or you don’t completely understand composite functions. Come see me or send me an e-mail and we’ll figure it out.

Here are a few sample problems and solutions.

We started today with reviewing the topics we started on Friday. We then went over ways to transform f into g by adding a new function every step. Plotting f o g was quite difficult but not completely out of the reach. We needed to take every number in the domain of g(x) and give it its’ value for g(x). After, we take g(x) and put it in f o g to find the solution. We also defined the domain and range for f o g algebraically. After todays’ lecture, we were assigned homework 1-4; 3,5,and 11 being the claim problems.