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

cos2= 2cos^2 - 1

Then after that, we were given these questions.

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.**

f(x)= 3cos2x-1

A= 3

B= 2

C= 0

D= -1

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

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)

## 3 comments:

Hi Jann,

I love the "Sine Dance"; another strategy to help with learning! I'm so glad you included it. Your illustrations also are such a good support to learning.

I have to admit I initially was aghast at how cold it was in Winnipeg, until I realized the readings were in celcius. I guess we in the US are the only country not using that scale. Now I've found a converter and checked your weather on the Internet, I can see you haven't had snow yet? (We're quite a bit warmer and have had snow as early as October 2.)

Your scribe is so very nicely done!

Best,

Lani

good job on your 2nd post jann! i think that this should be in the scribe post hall of fame! it's really good. very easy to understand. thanks for putting up the identities. I LOVE IDENTITIES! plus, you drew the SINE DANCE moves! awesome job.

be happy.

Nice Post Jann. I felt like I was in the class and your sine dances like a pro!!

Thanks for scribing.

Mr. Harbeck

Sargent Park School

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