Andy Schleb's scribe post

We started the class with the Supercorrection Follow-up test. That took the first 30 minutes of class. After that, Mr. Obrien put up 7 problems from the homework on the board. He let us go up to the board and do them, and then we went over each one.

A few key things:

• Use pythagorus to convert sin to cos (sin^2+cos^2=1), so (sin^2=1-cos^2, and vice-versa)

• Remember arithmetic (multiply/dividing fractions, equalizing denominators)

We then began work on a worksheet with four problems on it, to try and understand proofs. The goal was to turn the left hand side of the equation into the right hand side.

Finally, we had a class challenge in which we were given sections of trigonometric proofs. We had to arrange the in the correct order. It was a fun class!

Scribe Post 3.25.10

We worked on our Quarter 3 projects for 35 minutes at the beginning of class.

We went over the fact that we have a regular textbook homework assignment assigned today, but that on Monday even though juniors won't have class because of the science exam, our homework assignment will be to finish our final draft of the project. That is due on midnight on March 31. March 31 is also our supercorrection follow-up test.

Today we started Unit 6, which is continuing on with trigonometry. Mr. O'Brien put an equation on the board, and asked us to solve it either by graphing or by using a table:

We decided that x is all real numbers, except π/2 + πk, k∈Z

We then started working on proofs, and proved that the two sides of the equation were equal.

We looked in our textbooks at page 374 (the beginning of chapter 5.1) at the list of fundamental trigonometric identities. This included the reciprocal identities, quotient identities, Pythagorean identities, cofunction identities, and even/odd identities. I won't post them here because you can find them in your textbook. We went over the fact that:



Mr. O'Brien explained that

We went over the identities, and then looked at the examples in the book.

Ex. 1: Mr. O'Brien pointed out that the book doesn't use a triangle, but rather uses the identities. He said that he doesn't really care if, going forward, we use triangles or identities.

Ex. 3: Mr. O'Brien suggested that it could be easier to substitute a variable such as u for tan θ to factor something like this.

Scribe post 3/17

Today we got our tests back, reviewed question 9, and spent the rest of class doing supercorrections. Next class we will also have time to work on them, be ready to turn them in on Tuesday the 23rd. The homework is to work on supercorrections. Remember that our rough draft's of our quarter 1 projects are due on Tuesday the 23rd as well.

Weds. March 10, Last Day of Unit 5

Today, we began class by finding the equations for two mystery graphs. The first one had the equation which caused the graph to look like this:

The second graph's equation was which caused the second graph to look like this:

After discovering the equations for the two mystery graphs; we turned our attention to number 21 and 22 of Francois and his Pedometer. For number one we noted that =. After evaluating number twenty two we discovered that his set for all distances was 2.42 + 2k where k is an integer but also at 3.86 + 2k where k is also an integer.

Following the warm-up, our class reviewed Quiz 4 of Unit 5. The two numbers that we paid special attention to were number 1 and 4. For number 1, we noted that if you take and you added you would get , but if you added another you would end up with . This means, that all you have to do next is find the sin() which is . For number 4, one thing to keep in mind is that in functions, there is an opposite order of operations. This means that the easiest way to solve the problem is by finding your a, b, and c value then plugging them into a equation which looks like this: , the next step is to distribute your which makes a=2, b= and c=-.

Once we finished going over the Unit 5 Quiz 4 and any questions students had trouble on, we took the review quiz. The quiz will only count towards your quarter grade if you want it to. The quiz questions were the exact same as the ones on the previous quizzes. Next class, there will be the unit test covering chapter four. Mr. O'Brien suggested to students that they should challenge themselves while studying for the test by working on more complex and conceptual questions than the basic review.

The next class Scribe will be Tyler.

Homework question P. 359 #33 B

Hey Mr. O' Brien,
I am really confused about 33 B on page 359. I looked at the answers you have posted, but I was still really confused. I don't understand all the different aspects of the work to get the answer, like the B, Y, C, D, and other variables.

Scribe post

I'm sorry this is late but I've been having troubles with this posting thing.
To start the class we did a warm up where we had to evaluate

cos^-1(√3/3)
a) you would be looking for an angle and since you are looking for an angle where the inverse cos is a -√(3)/2 then it would be 150˚it is also possible to get an answer of 5π/6 algebraically you could do x=cos
cosx=-√3/2
sin(cos^-1 √5/5)
b) in this one the answer will be a ratio ø=cos^-1 sqrt(5)/5
cosø=sqrt(5)/5 sinø=(√20)/5

we also had to evaluate the graphs of
y=arscin(x-1)
a)y=arcsin(x-1) this is just a sin graph only with the restricted domain to make it a function and the negative 1 makes it move 1 unit to the right and the minimum and maximum is π/2
y=tan(3x-6/π)
b) you can set this up as an inequality because the period of tan is π so -π/2<3x-π/6<π/2>2π/9 y="sec^-1" secy="x" cosy="1/x" y="arccos^-1(1/x"

Consider Engineering

Great opportunity from University of Maine for this summer:

http://www.mainepulpaper.org/considerengineering/considerengineering.htm

Thursday, March 4 Class

We went over quiz, noting several things...

First, when Mr. O’brien says to graph both and angle and its reference angle in standard position, the initial sides of both angles must be on the x-axis. Second, much as sin(90º-θ)= cosθ, sec(90º-θ)= cscθ

After going over the quiz, we went on to discuss the inverse trig functions.

y=sin^-1x

y=cos^-1x

y=tan^-1x

Notation problems: sin-1x does not equal (sinx)-1

Because of this potential confusion, there are other notations to represent the inverse functions:

arcsin (x)
arccos (x)
arctan (x)

We saw that on grapher, arcsin(x) isn’t a function. On our graphing calculators we saw the inverse trig function is a portion of the entire function. We consider the inverse trig functions to be a collection of all the points possible while still being a function.
The same applies to Cosine, which doesn’t pass the horizontal line test any more than the Sine function does. A single Tangent wave passes the horizontal line test, and that is all that’s graphed of the arctan function.
Of course, all three graphs look different from the originals, since they are inverse functions, and therefore have reverse (x,y) coordinates.

Here are links to the three inverse functions. This should help make their domains and ranges pretty clear.

http://www.math.rutgers.edu/~greenfie/mill_courses/math151a/gifstuff/arcsin.gif

http://www.intmath.com/Analytic-trigonometry/arccosx.gif

http://upload.wikimedia.org/wikipedia/commons/f/f6/Arctan_plot_real.png


arcsin (x)
Domain: [-1, 1]
Range: [-π/2, π/2]

arccos (x)
Domain: [-1,1]
Range: [0, π]

arctan (x)
Domain: [all real numbers]
Range: [-π/2,π/2 ]

Use of inverse functions: We can plug in coordinate points along the unit circle, and the inverse function gives the angle. It gives angles in quadrants where that particular function (sin, cos, tan) is positive.

Then we took the quiz, which brought us to the end of class.

According to the tags on the side, Collin has only done one scribe post, so now it's his turn for next class.

Friday February 26th Class

Today in class we started off by taking the quiz.
After the quiz we went over some questions on the homework. We did problems 27 and 55.
27.


To graph these two functions we first looked at a standard sin graph.
http://fooplot.com/index.php
Then we took the f(x) function and altered the graph by moving the Y values of 1 to -2, and the Y values of -1 to 2. (Red)
We added on to that axis the g(x) function onto the same graph. This transformed the original sin graph by changing all the Y values of 1 to 4 and Y values of -1 to -4. (Blue)
file:///Users/student/Desktop/sin.tiff
The period is still 2π, and the symmetry is odd, as it is for all sin graphs. This means sin(-x)=-sin(x)
The transformation of these two functions changed the amplitude of the sin function.

55.
We then changed this to to make it simpler to graph.
This graph looked like: file:///Users/student/Desktop/cos.tiff
The period was 4π and the amplitude was changed, along with the graph being condensed. This graph originally (before being transformed) had was even, being symmetrical across the Y axis as all cos graphs originally are.

After reviewing the homework we moved on and looked at the graphs of the trig functions. We noticed that the sin graph and cos graph were very similar, but just shifted over to the right a bit. Both had a domain of -1 to 1 and a range of all real numbers.
We spent most of the rest of class playing with these graphs. We also looked at the graphs of the other trig functions as well and looking at the periods and amplitudes of the graphs.
We also looked at the tan graph which looks like:file:///Users/student/Desktop/tan%20graph.tiff

The csc graph which looks like:file:///Users/student/Desktop/csc%20graph.tiff

And the sec graph which looks like:file:///Users/student/Desktop/sec%20graph.tiff

But we did not get into why they are the way they are. That will be learned later and is in Dan's scribe post of class on 3/2.