graphing trig functions

GENERAL EQUATION

F(x)=a*sin(b(x-c))+d

KEY

a=amplitude (is a distance)
b=period (amount of occurrence in a given space)
c=Phase or horizontal shift
d=Plane or vertical shift

*note: a x-1 shifts 1 unit to the right, just as a x+1 shifts one unit to the Left, a positive x it just the -(-x), which make it a positive*

This is some fairly straight forward and basic stuff. The hardest part for me is remembering that -1 shifts right and +1 shifts left. Also i have to remember how to calculate the period of a function. That is the one thing that I have never really known how to do at all last year, and am finally learning it now for the first time.

I dont have a post for monday due to the fact that I put all my time into the class bolg. It can be viewed there!!

Solving Generally Over the Reals

Sometimes when solving trig equations, we will not be given a domain on which to solve this question, therefore there will be multiple answers from negative infinity to positive infinity. In a situation like this you have to coincide that any answer will occur every 2pi rotations (which is 360 degrees) with this in mind, we will have to make this known in out final answer. To do this we add on to the end of the answer 2kpi or kpi,(depending on how often it occurs). what this says is that for every K (which is an integer) rotations, this answer will occur to infinity.

Another Lesson Learned

Today we went over alot of examples similar to the questions found on exercise 4. I learned that when you factor a binomial expression (Ex x2+2x+1=0) there is the possibility that you could end up with an answer that looks like costheta=3 or anything that will cause a calculation error. In an situation like that you will completely ignore that part of the question, therefor the complete answer will solely come from the other half of the question. this concept in my head is similar to non-permissible values; answers that fit the description and seem to work out, but only cause you grief and despair!

Work Period

today we were given the oppurtunity to catch up on excercises, finish up our creations (the chart and unit circle) and were given a new blog assignment. I chose to work on my assigntments and got actually a substantial amount finished, For me lesson 4 was a lot of review, and I had to brush up on alot of my old algebra skills learned on the past. It is amazing how and what person will remember, even if you think that you dont know what you are doing!

Examples

We worked away at some accelerated math questions. Today I learned that angles that are over 2pi are actually very simple to solve. first you have to find the nearest degree in radians that you are familiar with that is closely related to the angle, i find that pi or 2 pi is the easiest. Next, all you have to do is add up the rest of the angles from that and eventually you will find an angle that you are familiar with that is within the 0 < theta < 360, from there it is just another simple trig problem that we have been doing since the start of the course.

Solving Trig Equations

today we started into the ever so loved trig equations. Although I seemed to understand most everything that Mr. Max was talking about, Alot of people didn't and therefore this class was a good refresher for me. All the Repetition and going over things made it so that the information presented was drilled into my head. We also learned how a trigonometric function can be put onto a graph. this is the basic function that will be always appearing throughout this course. I learned a bit more on how exactly to solve where each asymotope is and also more importantly how to solve a question that involves several answers cause the question has a set limit. I found this class very useful because asside from this i also got 1/2 of my chart finished!

Exact Values

Thursday, September 17, 2009

Exact values is just a really technical term for a value at a specific, given location. The trick to these is to first evaluate where on the unit circle the angle is. We can do this by just remembering what we learned about the unit circle in previous lesson, and just expand our thinking just a bit. for example: 17pi/4 looks impossible, but if you think that pi can be didided into 4 and a inverse fraction is possible because we are more than only one pi. Once i can grasp that principal i had no problems when working my way through lesson 3. An exact value, if refering to a unit circle, is just a coordinate on a plane, and depeinding if you are asked to find the Sin Cos or Tan, the coordinates will always follow a type of pattern (as i found from working on the chart we were asked to make).

Creation of the Unit Circle

- Extremely logical
- If you know fractions you should be able to solve this Unit Circle

Six trig ratios:

Sin=y/1 Cosecant=1/y
Cos=x/1 Secant=1/x
Tan=y/x Cotangent=x/y

*memorization of inverse terms is important*


The second time around in this class allows you to catch all the tiny bits of information that slipped by the first time. What I learned this class is that I need to think less about the question and focus more on the principals that I already know, cause everything that Mr. Max teaches us can be applied in some way to the questions we will encounter in the future on tests and the Final exam. The trick is to go outside our traditional thinking areas and try to come up with something new that we havenet really thought of before.

Work Period

Because of our lack of computers in the cafeteria, Iwas not able to make a post, so I am doing it today. Well yesterday we had a substitute teacher, therefore it was a period where we could "catch up" with out old work and also start into out accelerated math packages. Basically I just finished up my exercises 1 and 2, but need to get some accelerated math so I can get that done. Helping others will also, even though you may not know it at the time, help yourself as well. Now that is the main thing i have learned today!!

Circular Functions (unit circle)

- Co-terminal angles will always end up at the same place (exact same terminal angle), only one runs cw and the other ccw
-S=Theta(r)--------(S=arc length, Theta=inside angle, r=radius)
- Unit Circle implies the radius at any point along that circle is 1 unit long
- sides x and y on the unit circle are easily calculated using simple grade 11 trig or Pythagorean theorem
- cos=x, sin=y (x,y)
- The hardest part is just understanding that the circle isn't just something to be memorized, it is actually to the contrary very logical and can be be thought of as just fractions

Radians

-3 and a little bit radians (3.14) is equal to 180 degrees
-Pi radians=180 degrees
-2 Pi radians=360 degrees
-one radian=57.3 degrees

My Goal

well to begin this is my second kick at the can for math, but this time my goal is very simple, a 90%+ average so i can eliminate my first year university and go straight into it. I will definitely be able to concentrate alot more on my math now as i only have one class in school this semester. If it means that i will have to stay after school some days or even come in on the weekend for tutoring, well than so be it. This class will be my to priority for this part of the year and hopefully all goes smoothly.