Wednesday, February 18, 2009

Time to Reflect on the Past........

Hello to all you Pre-Calculus enthusiasts and to those visiting our blog! Good evening (or morning/afternoon depending on where you are)! I figured that I should probably do my reflection now before I forget about it later so here goes!

I'd like to start off by saying THE SCRIBE LIST IS UP! There are a few things you should know. In order to be officially crossed off the list your post must be fully completed and correctly tagged! This means that your name cannot be crossed if you say that you will when you get home. It has to actually be there and complete. Also make sure that when you tag it you put (THE UNIT TITLE), (YOUR NAME), SCRIBE. That way you get credit for doing your scribe post. (:

As far as circular functions go in our class, I feel that everything was pretty straight forward. I like the way that Mr. K lets us see where all of these numbers and formulas come from like π, sine, cosine, tangent, cotangent, etc. I think it's pretty cool how we get a math lesson as well as a history lesson! I also think Mr. K has a really great point. Instead of memorizing everything (like the sine value of 5π/6), remember the relationships like where they are in the unit circle and the root 1, root 2, root 3 pattern in the numerators in both sine and cosine. I know that's what helped me get through this unit! (:

The hardest thing during this unit was probably the grade 11 review questions. Now I know what you're all thinking. "Really? Are you serious PJ?" Why yes folks, I am dead serious. I think it's just the fact that I haven't done any streneous Pre-Calculus work in a year and that my mind is just slowly bringing everything back from grade 11 as time goes on. Well I know chemistry and physics involved some math but it wasn't like hardcore Pre-Calculus-type math. But don't worry, I'll remember eveything (eventually!) !.

So yes, I guess now is the part I should give you all advice on the test.

Don't forget any of the basic stuff like circumfrence (2πr) and area of a circle (πr^2). Haah I'm sorry if it sounds like I'm contradicting myself with the whole formula stuff and yea but sometimes there are things you should just know.

Keep the image of the unit circle in your head. Remember the relationships of sine, cosine, tangent, secant, cosecant, and cotangent. Remember SOHCAHTOA and CHOSHACAO (LOL Matthew!). That or you can remember the whole C+S pairs, like Cosine and Secant.

If a denominator has 0 it's undefined. If you have to find the square root number there are two answers (just as SheldonCooper said): one negative and one positive. If you have to solve for more than one x value and one is undefined (like sin x= 0.7384 and 2 but sin (x) can't equal 2 because it's maximum is 1), make sure that you explicitly state that.

Remember that when you have to find angles that there is usually more than one answer like for:
sin (x) = 1/2
x = π/6 and 5π/6

Of course you have to keep in mind the intervals. In my above example, my interval was [0, 2π]. If you have to solve for "all real numbers" use 'k' in your answer. For example:
Solve for 'x'. 'x' is an element of the real number set.
tan(x) = 1
x=π/4 + kπ where 'k' is an element of the integer number set

Don't panic! Stay relaxed and don't fret if you can't get the answer right away. Skip it and move on. It'll come to you eventually.

Take your time! Don't rush! Double check your answers and make sure you did everything right. There's no harm in checking your work. In the end it'll probably be beneficial for you!

Well I think this post is getting a little bit too long. I won't actually be in the room doing the test with all of my wonderful classmates as I, along with Dion and Rebecca will be at S.E.T. that entire day. We still wish you all the best of luck on the test! We're with you guys in spirit! xD


  1. for "Solve for 'x'. 'x' is an element of the real number set.
    tan(x) = 1

    since tan is positive, should not x=π/4 + Kπ where k is an element of integers.

  2. haah thanks for that! i will edit that right now xD

  3. Hi Jayp,

    Great reflection and one of value to all I'm sure!

    Now that you've completed the reflection, is there something in particular you learned from it?


  4. Hi Lani!

    Aside from the various history lessons provided by Mr.K, there are a few important things I found out, not only about math but about myself as well. For the math part, I learned an easier way to figure values on the unit circle for sine, cosine and tangent. I also learned about secant, cosecant and cotangent and their relationships to the other three functions. I found the graphing quite annoying, but it wasn't hard.

    As for what I found out about myself, I think I need to really bone up on my grade 11 math. After all what's a building without a good foundation right? Also working in groups really helped. I could see what I did wrong and other methods of solving problems.

    Thanks for the comment Lani! I look forward to your next input on our class blog.