Link for Wednesday, May 5th

http://www.pa.uky.edu/~phy211/VecArith/index.html

Today we started with a homework quiz.
Then we proved why

We used Pythagorean theorem for the right triangle:

and we got that:
Then we used Pythagorean theorem for the left triangle:

also we used to get
Then we substituted everything from the left triangle in the equation we got for the right triangle. So the final equation is:
It works with SSS and SAS.

The next part of the unit were vectors.
In math the vector is a segment with direction, also called directed line segment:
The first point of the segment is called initial point (A), and the last point is called terminal point (B). a, b are components of the vector -
The length is sometimes referred to as magnitude,
Using Pythagorean theorem we could write it as:
The angle of the vector, θ is called direction angle.

examples:
1)Find the component form for a vector with initial point (-2,4) and terminal point (3,1).
The answer is <5,>

2)Find the component form for and θ=45º
, so
, so
The answer is

The rest of the class we went over hw.

Today in class we did a lot of things. We started with a warm up that asked us to find the triangle with these given sides and angle:
A=26º
a=5
b=8
This gave us an ASS (angle, side, side) case, which we know presents an ambiguous case. An ambiguous case provides you with information that you could use to create two different triangles. During this warm up we were asked to solve each angle and side of this triangle along with its area. Students could have solved for two different triangles with these given sides and angle. After the warm up we explored and proved the ambiguous case by constructing a visual of these possible triangles on Geogebra.

As you can see in the visuals there are two different triangles with values:
A=26º
a=5
b=8
This proves the ambiguous case.
We calculated the other possible sides and angles using the theorem that:




By Monday we are to prove that (when given SSS or SAS):



(and also find the largest angle when given SSS)

And for Bonus points we have the option to prove Heron's Area Formula (when given SSS) of:
, where s is the half perimeter.

Homework for 4/29

Some of us didn't understand problems 41 and 43 from the previous hw. Could you please post them here? Thanks.
Petra

Links for Thursday, April 29th

http://www.geogebra.org/en/upload/files/english/dtravis/ssa_ambiguous.html

http://home.comcast.net/~paulbirdsall/class/ambig.html

Scribe post, 4/27/10

We started with a warm up where we had to
1. Solve on [0,2π)
sin2x-cosx=0
2. Find the exact value of cos105˚
3. Use the figure to find tan2u
















We went over how to figure out if our answer is right when we finally get an answer.
For number 1
sin2x-cosx=0
2sinxcosx-cosx
cosx(2sinx-1)=0
so cosx = 0 and sinx = 1/2


for number 2
cos(105˚)

we then went over the Law of Sines which is and
we started deriving the law of sines

then we proved that they are all equal for all triangles

We also talked about the added bonus which is

we tried this on a random triangle from GeoGebra where (using AAS therom)
A=59.85˚
C=26.05˚
c=4.78 units

so B =180˚-A-C
B=94.1

so a = 9.41

b=10.86
for the last 10 minutes of class we did our homework

April 16 scribe post

Mr. O' Brien reminded us to spend a solid hour on math homework, so that on quizzes we would not be stuck on the problems by not knowing what to do in the beginning as the first step.

We began class with a warm-up:

We were asked to attempt to graph this without technology. So...

This is what we would have gotten if it originally was a positive tan. However, the negative makes it more difficult.

Therefore...

This makes us able to graph this equation by hand.

After the warm up we went over homework problems. We covered #33,77,29,75,

While doing this we went over the identities that we needed. #75 is the most important question on the homework, and there will probably be a question like this on the unit test. Make sure that you know how to do this problem!!! Remember to draw a triangle to help you get through it. If you don't know how to do this problem yet, then go to the download and try to work through it until you think you have more of a handle on it, then try and do it by yourself until you know that you could do this problem by yourself on a quiz or test.

While still working on this problem 75 we started to learn to put the sin, cos, and tan answers into the calculator up on the board. Then, we checked all three of these on our own using our own calculator. The sin, cos, and tan were:

inverse sin(-4/5)
inverse cos(-3/5)
inverse tan(4/3)

Put them all into your calculator and you can see for yourself that they are correct, and that the inverse sin and the inverse tan equal the same value.

The last thing we did in class we all took out our quiz and the homework's it related to Mr. O'Brien came around to people individually to help us understand what we missed.

Our Goals were:
Correct Each..
Quiz questions
either on quiz or in notebook using HW #3,4,5

Class was only an hour because we have the Bunny Bowl later on today.

Collin will be the scribe for next class.