Trig Identities - Sum and Difference

Today we continued on with the Trig Identities unit and into a section called "Sum and Difference Identities". Today basically consisted of us learning six formulas using sin, cos, and tan; and how to solve angles that we are unfamiliar with, such angles as 7pi/12 and tan(75) (for the formulas, refer to the formula sheet. All these formulas will be given to us on the final exam, so know them, DON'T MEMORIZE THEM). A sum and difference question can be looked at as being a 2 part question. What I mean by two part question is that there is more that one piece to the problem, and furthermore by piece I mean angle. Up until now we were familiar with angles like pi/6, pi/4, pi/3, etc....... and never really thought of having a twelfth of a pi. Now comes the thinking part. "I don't know a thing about pi/12, but since this angle can be thought of as a 2 angle identity, mamby two angles I already know can add up to a twelfth..!!" Now we are on to something, two angle we know are pi/3 and pi/4, and added together equal to 7pi/12. Well that seems pretty easy some would say, but some question will take a little more effort that that to be solved. Unfortunately the only way to come about finding these answers is by educated guessing and checking. Mr Max said that solving identities was like doing a puzzle, so let the puzzle sloving begin. Use the angles you already know on the unit circle and take some previous fractions knowledge, put them together to figure it out. when you find the two angles that add together or subtract from each other, go to the formula sheet and find the corresponding formula. when you have the formula, set one angle to alpha and one to beta, AND DO NOT SWITCH THEM AROUND. Plug the alpha value into everywhere the alpha symbol appears in the formula, and do the same for the beta value. from here all you are solving for now is exact values that come strait off the unit circle. Follow throughout the formula and complete all the algebra taking into consideration the order of operations, and eventually you will end up with an answer. (haha I know, convincing eh??) The trick is practice, and the must is remembering algebra rules.

If you need help ever and don't have a teacher or tutor at your right hand, there is a new sight on the net called wolfram alpha (http://www.wolframalpha.com/). this site virtually lets you type in any mathematical question and it gives you the answer in about 15 different ways, and it can even graph it!! try it out for yourself and see what wolfram can do for you!!! This has been a paid advertisement for wolfram alpha inc. jkjk Mr. Max told me to put it on. so i did....

Anyways, The homework for today was Exercise 16 #1-15, but omit #3 & 5, and remember that there will be a homework check sometime next week on the lessons 11-20.

Reciprocal Functions

Recripocal functions can be defined as;

a/b --------> b/a

In today's class we learned the basics of a reciprocal function. Mr. Max refreshed the class on reciprocals using some grade 11 examples, learned that a reciprocal function is one in which the numerator and denominator switch places, and learned algebraically how to do this. The tricky part came when we put this thing onto a graph!! The graph of a Reciprocal function, compared to it's initial function is curved and has one or more asymptotes along the x axis. The asymptote of the reciprocal function is found where the initial function crosses over the x axis (the x intercepts). Near each asymptote the reciprocal function behaves in a manor opposite to the initial function. What this says is that if the initial function increases as it approaches the asymptote, the reciprocal function will curve off and get smaller as it approaches the asymptote. Similarly, if the initial function decreases, the reciprocal function will increase. The terminology given to was GREATERING and LESSERING (this is a "mathematical technical term" and is not real english, haha). the most important part to remember when deciding whether each function greaters or lessers it to read in the same direction to or from the asymptote. If you read it differently and switch directions at any time, none of the graph will be correct.

Work Period

Today, as mentioned above, was a work period due to the fact Mr. Max was not here. We were given the opportunity to catch up on any homework given over the past couple weeks, finish up late assignments such as out charts or unit circles, or else continue working on our accelerated math. I am advising you, my class, to keep on top of your due exercises and especially accelerated math! There are a few ways to get free marks in this class, and you CANT afford not to get them. These free marks can account for a substantial amount of your final grade, and in some cases can even mean the difference between a pass and fail. So try you hardest on these sections of this course. Secondly, I would like to strongly advise that if you don’t understand the material as it is being taught, take a little time to stay after school and go to a tutoring session. In most cases you will learn more there than you would ever learn in one class. You have nothing to loose and everything to gain, and besides you cannot get less intelligent! I tell you this cause I am speaking from experience, and I only wish I would have known these things the first time around. I believe that if you do these things and try your hardest, this course will go smoothly for you and you will be satisfied with the results. There will be a test this Thursday, so be aware that we will be having our first homework check in the next few days!!