More Double Angle Identities

Today we were given a few more examples of double angle identities. I used to think that I understood what I was doing but now I'm not too sure. I get confused because I keep forgetting to look at my formula sheet and look at the identities and pick one that will work for the question I am working on. Boo :(

Finish Exercise 18 and work on accelerated math.

Work Period

Today we had a work period, I was very happy!
Test is moved to Thursday now, not Wednesday. Once again, I was happy :)

Double Angle Identities

Today we learned 5 new identities called Double Angle Identities. I understand this. Woo hoo...... ! Trig is Awesome.

Sum & Difference Identities

Today we learned 6 more identities called sum and difference identities. We used the example of 7pi/12 and how it can also be said as pi/3 and pi/4, so those two new values can be put into the corresponding sum/difference identity.

Homework: Exercise 16, questions 1-15 (except 3 & 5)

Extraneous Roots and More Identities

Well yesterday I was understanding almost everything that we were taught, but today I can kind of confused. I think all I have to do is somewhat memorize all of the identities and then it will help me with my work.

We were taught today that an extraneous root is a root that works on paper until it is checked and proved otherwise either through squaring or by other raised powers.

Trigonometric Identities

This is what I learned about identities:
-An identity is an equality that evaluates as true for any value of input.
-Trig equations that are not identities are called conditional equations
-Graphing is not adequate to prove "identity-ness", however, graphing is enough to disprove it

Basic Indentities are:
csc (x)= 1/sin(x)

sec (x)= 1/cos(x)

cot (x)= 1/tan(x)

tan (x)= sin(x)/cos(x)

cot (x)= cos(x)/sin(x)

Simplification Techniques to Assist Proving are:
1. Reduce complicated side to try to match the simpler side
2. Work each side independantly to some intermediate expression
3. Do addition/subtraction of the rational expressions
4. Do multiplication/division of the same rational expression
5. Simplify GCF's always
6. Factor! Factor! Factor!
7. Try multiplying both numerator/denominator by the same expression (to get known identities)
8. If possible, rewrite all trig functions as sin (x) or cos (x), look for patterns

Review

On Friday's class we were given Exercise 12 to work on. As we worked on our assignment, Mr Maks was in the cafeteria doing a homework check. We would each take turns going down one by one and we would chose 1 assignment at random to show him and he would give us a completion mark out of 10. The assignment I had to show him was Exercise 5, and that was an exercise that made noooo sense to me. I was given the mark 4/10, but Mr Maks gave me a website to check out and see if I could understand what I was supposed to do. I looked at the website and all of a sudden everything made sense! I finished the assignment and showed him again and recieved a better mark.

In today's class we got our tests back from 2 weeks ago, and I was happy with my mark. I got 46% and I actually thought that I did alot worse, so I was happy with the 46%. We were also given an answer key, so this way I can go back and correct mistakes, and also see how Mr Maks expects us to answer the questions. We were also given the answer key to the pre-test (with the superman cartoon on front) that we recieved last week which is similar to the test that we will be doing tomorrow! I'm not quite sure how I am going to do tomorrow, so I am deffinately going to look over the pre-test and then the answer key. Another thing I did today was finish the first 23 practice questions on Accelerated Math! I am testable in 2 objectives, so hopefully I will get that done soon and my mark will go higher. I am at 71% as of today, and I would like to keep it there or higher, no less than 70% for me!!!

Absolute Value Functions

Today we learned how absolute values can be understood as a piece-wise function (the function can be split into one or more pieces).

Definitions of an Absolute Value:
|x|= x if x is greater than or equal to 0
|x|= -x if x is less than 0

Example: When graphing y=|f(x)| :
|f(x)|=f(x) if f(x) is greater than or equal to 0
|f(x)|= -f(x) if f(x) is less than 0
The domain of |f(x)| is the same as the domain of y=f(x), but the range of y=|f(x)| will be f(x) is greater than or equal to 0.

I don't think I am making any sense... so I found this website that may help.
http://www.analyzemath.com/Graphing/Graph_Abs_Val_Func.html

Assignment: Exercise 11, Questions 1-12

Reflections and Graphing Reciprocals

Yesterday we learned about reflections (flips). I wrote everything down but I didn't quite understand what was going on. I will watch the recording tonight and hopefully understand what was taught to us yesterday.

Today we learned about reciprocal functions and how to graph them. We observed that:
1. f(x)'s x-intercept is 1/f(x)'s asymptote.
2. In the same interval (left to right, or right to left) f(x) is "greatering" and 1/f(x) is "lessering" (or vice versa).
3. It seems the at values of y=-1 and y=1, the graphs of f(x) and 1/f(x) are at the same place.

Translations

On Friday's class we started a new unit on Translations. We learned that translations are slides and only ever move left-right, up-down, or a combination of one of each. Today we continued learning about translations (horizontal stretches/compressions, and vertical stretches/compresssions).