Scribe Post: Day 15

Hi guys! This is Jann(again) and I'll be your scribe for today. (^_^)

Today we talked about Identities.

Fundamental Identities:

tangent= sine/cosine

cosecant= 1/sine

secant= 1/cosine

cotangent= cosine/sine

Pythagorean Identities:

sin^2 + cos^2= 1

1 + cot^2= csc^2

tan^2 + 1= sec^2

Sum & Difference Identities:

sin(a+/-B) = sin a cos B +/- cos a sinB

cos(a+/-B) = cos a cos B -/+ sin a sin B

Note: Mr. K showed us how to do the "Sine Dance". It will help us remember the formula. The actions are like this:

Double Angle Identities:

sin2= (2sin)(cos)
cos2= (cos^2)-(2sin^2)

cos2= 2cos^2 - 1

Then after that, we were given these questions.

1. Sketch the graph of

If you look at the properties, you should have something like this:

The properties are:

- shifts the graph up by 1.

- reflects the graph towards the x-axis.

- shifts the graph to the right by 1.

Note: The formula of the period is:

Note: The standard form for a sine function is f(x)= AsinB(x-C)+D; where A=amplitude, B= Period, C= face shift, D= vertical shift.

2. Write 2 equations, 1 sine and 1 cosine for this graph.

The class came up with these 2 formulas:

f(x)= 3cos2x-1

A= 3

B= 2

C= 0
D= -1

f(x)= 3sin2 [x-("pi"/4)]-1

A= 3

B= 2

C= "pi"/4

D=-1

Lastly, we plotted this table in our calculator.

Note: This information is real! Its based on the real average temperatures in Winnipeg.

Here are the steps to graph this table:

i) Make sure your lists are clear. Press [2nd] then [+]. Press [4] for "ClrAllLists".

ii) Press [Stat] then [1].

iii) Enter the numbers on the table. Month in L1 and Temperature on L2.(Note: Plug in no. "1" for Jan, "2" for Feb, etc.)

iv) Press [2nd] then [Y=]. Make sure your plots are on and on the right list number.

v) Press [Zoom] then [9]. Hit [Enter].

To calculate the reg,

-Press [Stat] the arrow right to "Calc"

-Arrow down till you see "SinReg".

-Enter L1, L2, Y1. Hit [Enter].

You should see something like this:

y=a*sin(bx+c)+d

a=19.49038889

b= .4657581446
c= -1.720934653

d= .5227365909

I think thats all we did today. Whew....(-_-)

Finally, if there's something wrong, please with the capital P, post a comment.(^_^)

Oh, and the next scribe is Charlotte! (cuz your the last one on the first cycle)