scribe post-bekah-chapter 2 and 3 catch up

Monday, March 15th.

Today we went over sine and cosine in more detail.

Jojo wrote this equation on the board:

y=a sin (x-h) + k

if y=sin x

and we were supposed to figure out what a, k and h were.

h=0

k=0

a=1

We learned that the amplitude is the height of the degree axis to the highest part of the function. So pretty much, amplitude = the highest point

If you are given y = 2 sin x than the amplitude (a) = 2

The amplitute would also = 2 if we were given y = -2 sin x, because the highest point on the degree axis would still - 2

We than began going more into the amplitude, with more depth.

We figured out that a = a positive number if the line on the graph goes up from the origin.

We then figure out that a = a negative number if the line on the graph goes down from the origin.

We started vaguely going over the other parts of the equation (y=a sin (x-h) + k) that Jojo gave us earlier.

From this we learned that h decreases if it translates horizontally (left or right.)

Jojo told us that the difference between sin(x) and sin (x-0.6) is that one the graph it shifts differently.

-->it's all about the shift.

When h = a negative value (x-h) = (x-(-h)) so it = (x+h) shifting to the left.

We also learned that h is done in radians.

Tuesday, March 16th.

We first revisited the AMPLITUDE, and clarified that you can find the value of the amplitude by the distance between the x-value (0,0) to the highest point (on the y-axis) or the lower point (on the y-axis.) You measures the midpoint to the highest or lowest y-values. We learned the equation you can use to find the amplitude:

the absolute value of 1/2(max y-value - min y-value)

We then learned what the Sine and the Cosine Graphs look like.

y = sin(x) the graph goes through the center origin (0,0). Going up (on the right) one unit up, one then

one unit down, then one unit down again, then one unit up, then one unit, then one unit

down, than one unit down. The left side does this same thing, but first it goes down and then

goes up and than goes up and than goes down, etc.,

(You should be seeing a pattern on the graph in your head)

-We also learned that another way of finding out what the graph looks like is by using your calculator.

You press the button that has: y= :on it. You then plug in whatever you are given. Then you press

the button that says: GRAPH :on it. There you will have the graph for your sine or cosine equation.

y = cos(x) the graph has the same pattern, except it starts on amplitude of the positive part of the y-axis therefor

going down symmetrically on each sides.

-You can also use the calculator to figure out the graph for the cosine equation.

Wednesday, March 17th.

We learned went over some main Identities today and then practice some problems.

The first identity we learned about was the:

Reciprocal Identity: sin x = 1/csc x csc x = 1/sin x

cos x = 1/sec x sec x = 1/cos x

tan x = 1/cot x cot x = 1/tan x

Jojo then showed us what tanx and cot x are in terms of sine (sin x ) and cosine (cos x):

tan x = sin x/cos x

cot x = cos x/sin x

The second identities we learned about were the :

PT identities: sin^2 x + cos^2 x = 1 --> divide everything by cos sin^2 x and you get

1 + cot ^2 x = csc ^2 x --> cot x (this leads back what Jojo taught us about the cos x)

sin^2 x + cos^2 x = 1 --> divide everything by cos ^2 x and you get

tan ^2 x + 1 = sex^2 x --> (this leads back to what Jojo taught us about the tan x)

Pretty much everything we learned upto here, today has been been the identites that lead back to the sine and cosine.

We then walked through problems 1, 2 3, 4 and 5 on Page 173 in our Trig Textbooks)

-During problem 5 we ran into FOIL-ing, which is a math technique that most of us learned from Algebra. To FOIL you foil down the problem:

(a - b)(a+b) --> you foil the equation. a * a, a * b, -b * a, -b * b, which gives you a^2 - b^2

Thursday, March 18th.

Today we learned how to find the coordinates on sine waves.

Friday, March 19th.

Today Jojo was ready to teach us about EVEN and ODD Functions:

On the board he had two sections of information written down:

1.) EVEN--> symmetric about the y-axis

cos(-x) = cos(x)

sex(-x) = sex(x)

2.) ODD--> symmetric about the origin

sin(-x) = -sin(x)

csc(-x) = -csc(x)

tan(-x) = -tan(x)

cot(-x) = -cot(x)

We than went over some examples from the book: Page 173 problems 24 and 26. We walked through each step of every problem.

24. sec(-x) - sec(x) -->we have to solve and we know/see that in normal math the answer would = 0 and that is completely correct. The answer is 0

25. cos(y) + cos(-y) -->this turns into

cos(y) + cos(y) --> which equals

2cos(y)

We than learned a few random things about EVEN and ODD functions.

-if you fold an EVEN function graph: f(-x) in half the sides will line up perfectly. The graph will have the same y-values on the positive and negative sides of the origin.

-EVEN = f(x) = cos(x)

_ODD = f(x) = sin(x)

March 22nd
Today we went had a daily quiz and then began learning about STRATEGIES in trigonometry.

Jojo states that "it's really a crazy puzzle but there's a method to the madness" -which was exactly what we began doing during class.

Jojo first showed us the strategy that uses:

VERIFYING IDENTITIES: 1 + sex(x) sin (x) tan (x) = sex^2 (x) -->(this is the identity and now you must verify it)

Step 1: Start with the most complex side and work towards the easier side.

1 + (1/cos(x)) (sin (x))(sin(x)/cos(x)) --> here we turned everything into sine and cosine)

Step 2: Divide everything by the cosine --> sin^2(x) + cos^2(x) = 1

1 + (sin^2(x)/cos^2(x)) --> 1 + tan ^2(x) --> sec^2

-If you didn't notice there are a lot of Reciprocal and PT identities--this shows us how important it is to really have the identities down-

We then went over Identifying the Factor for the different of squares:

The first thing we covered in this section was:

FOILING: any time you have (a^2 - b^2) it also equals (a - b) (a + b)

The second thing we covered in this section was:

PERFECT SQUARE BI or TRINOMIALS: (we couldn't figure out if it was bi or tri)

(a + b)^2 always simplifies to a^2 + 2ab + b^2

We were about to begin figuring out the RATION EXPRESSION but it was time for Monday Morning Meeting.

I am terribly sorry for this scribe hold up, i promise never to do it again. I hope that my scribes from last week are helpful to anyone who may need it.

The next scribe is..zoe