March 26th Pre-AP Calc Fun

Today we started off with a Supercorrection Follow-Up Test which took up thirty minutes of class. We then quickly debriefed the Aspirations Fair. After that we went over a few homework questions. We planned to work on projects but we ran out of class time. Remember the projects are due March 30th!

Project Help: To label an axis on your graph go to inspector then physically click on an axis then click on or off label.

Homework Questions:
One example of a problem,
25. --> sec part can be simplified as
then

Homework: Project due March 30th by midnight.

SuperCorrections Follow-Up Test

Does anyone know where or if there is a link that has a blank test to practice with? Please let me know! Thanks

Trigonometric Identities: 3/24

We spent the first half of class working on our projects. The rough drafts are due today!
Then we did the warm up.

Solve graphically/numerically:






The graphs were the same, so this equation is actually an identity.






Making a proof for this identity:




= Left hand side


= Right hand side



More on Identities
on page 374 has list of fundamental trigonometric identities (this will be your Rosetta Stone):

• Reciprocal
• Quotient
• Pythagorean
• Cofunction
• Even/Odd

Homework:
page 379: 9-65 (by 4's), 77, 93

Kayla will be next scribe!

March 18, 2010

NOTICES:
-If you have finished your supercorrections, then you can pass them in tomorrow to have the graded over the weekend. If NOT, then that is fine too. The extended due date for supercorrections is MONDAY.
- The Quarter 3 project rough draft is due on Monday as well.

Today in class we worked on supercorrections. If you have any questions, pertaining to supercorrection answers or project problems, find a classmate or Mr. O'Brien for clarification. Have a great weekend!

March 16 2010

We started class today by looking at the project. We're supposed to have worked for an hour on it, and just keep working on it. We talked about number 4 a little bit, Mr. O'Brien reminded us to make the scale on the y-axis correspond with the graph, so that the window shows the entire graph.

Next, we looked at the test, and started super-corrections. We specifically went over number 9. This was the question that said to let p=sin40º, and let q=cos110º. For these problems, its helpful to draw a diagram, and draw the angles and their supplements.

Since the y-coordinate of each of the black points is p, sin40º=sin140º, so for question a, the expression for sin140º, is p. I'm still a little fuzzy on this one, but I think there's a bunch of people in class who get it more.












We also talked about number 12 on the test, the question about phase shift. The question says to find the phase shift of the graph below, which looks like this:

For this problem, it was first necessary to find the equation, and then put it in the right form. Then you could plug in k and c into -c/k.

For the rest of class, we continued to work on supercorrections, and will next class too. The homework is to keep working on the project and the supercorrections.






Next Scribe: Marnie :)

Review Day!

We started off with some warm up questions that were labeled as "test rejects!". They were pretty tricky, so Mr. O'Brien made them worth extra credit. The first one ended up having the equation , and the graph looked like:











The second tricky graph had the equation and the graph looked like:



















These graphs were tricky, but they reminded us that we have to think about all math functions when taking the test, not just the six basic trig functions. After completing these graphing warm ups, we continued with our friend Francois as he kept biking around his neighborhood. We figured out numbers 21 and 22 in the packet, and made a few big connections, like how
= .

We then went over some homework questions and questions from past quizzes. We went over the conversions from angles to DºM'S'', which you find by multiplying the fraction of a degree by sixty, and if there is a decimal, by sixty again. We reviewed the "skiing down a mountain" problem from quiz three again, which is easily solved by using the inverse sine function. We also realized how important it is to make sure your calculator is in the right mode when solving problems (e.g. using degree mode on the ski hill problem). This is something to watch out for on the test!

We then took the review quiz, which only counted if we wanted it to! The quiz was made up of questions that had only been on previous quizzes, so if we had put some time into studying the quiz was a relatively easy grade. The quizzes were ready to be picked up by fourth period, so if we needed to, there would be time to review any of the quiz concepts we still had a hard time on.

The test is next class, and will cover all of chapter four. This is a ton of information, and I feel like it might be a little harder than some of the other tests because of all of the different functions. I'll really need to focus to remember things like how the graph of the cotangent is different from the graph of the inverse of the tangent. The homework for tonight is to choose a minimum of 8 review problems from pages 356-369. Mr. O'Brien left a warning on the iCal to not only do the easy problems. Especially in preparation for a test with on much information, it would be really beneficial to do some problems you have to think through. All unit homework must also be turned in before the test on Thursday, so make sure to organize it. Have fun studying!

The next scribe will be Hannah!

Consider Engineering

Great opportunity from University of Maine for this summer:

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

Friday, March 5 - Last Day of Unit 4!

Last Day of Unit 4 :)

Today we began class with the following warm-up:

1)Evaluate.
a)



*Remember to put your calculator in radians.*

Is it 5π/6 or 7π/6?
We found it's 5π/6, because you will never find it in quadrant III. With inverse cos, the answer will never be negative. It's range is only positive values. Check your calculator to back your thinking. We talked about how there's a major difference between inverse sin and inverse cos.

b)



Answer was sqrt(6)/6 or 0.408. One way to solve this:
Maci gave a good way to solve this, but since it says "evaluate" we can just use our calculators.

2) Graph.
a)


b) Go to p. 352/102

For these, use calculator, geogebra, or even Mr. O'Brien's http://fooplot.com/index.php to check your answers.

*The only difference between a and b, is that b is shifted over one to the right.

We went over how


actually means


WHOA!!!
Just like how



can be entered into your calculator as...




After the warmup, we went over the quiz and any problems people had. Remember, if you guys are struggling, if you're getting a 20/30 or even a 15/30, that's ALRIGHT! You're on the right track and getting it.

"When you're in college, you'll just be focused on math! It'll be wonderful! It's like heaven." -Mr.OB Quote of the Day (3/5/10)

Applications:

Simple Harmonic Motion: (check out p. 356)



Bearing:
Ocean/Land:
*Always an acute angle.
ex. S 85 (degrees) E

Air:
*Always between 0 degrees and 365 degrees.
ex. 095 degrees

Look at #33 on p. 360.


For next class, practice on p. 359/29, 53, 31, 57, 59 (from HW!).
Remember, we have a quiz next class! Study any old quizzes, because all the problems will be coming directly from the old quizzes. Our unit test will be next Thursday, and ALL our unit's homework will be due.

Alright...signing off...
Happy studying!

Next scribe: Caitlin :)))

March 3, 2010: Quiz Day! (Again..)

Today started off with a nice warm up involving the graphing of tan functions... by hand. I don't know if anyone else knew this little trick we learned in class, but I just learned it this period & personally, it's demystified a lot of the stigma of graphing tangent functions:

1. Take the simple equation of:

Substitute in your own equation (whatever is in the parentheses, simplified).
2. Solve for x.
3. The equation now gives you two asymptotes of the function. By plotting the intercept directly between these two asymptotes, you've gotten yourself a period! Yay! Just repeat for more periods.

EXAMPLE:

Simplified:

*Remember that the order of operations are switched!*
1. Write your inequality using your simplified equation.



2. Solve for x.





3. Graph!


Ta-Da!

Then, we moved on to some review of the homework, & that went pretty smoothly. We covered 23, 43, & 75.

Afterward, we began a new section of trig.. INVERSE TRIG FUNCTIONS.
Here's an example:





Basically, that's how you would work through having an inverse trig function.. We didn't really get that far, unfortunately, because we had to go to lunch & then we had a quiz to take, so I can't really write much more :[ Speaking of, the quiz went all right, but there were a couple of tricky problems that I really had to think through. Did anyone else struggle with a problem or two?

No homework tonight, but it'd be smart to look over the project!! Next scribe is Anna. <3

What Could Have Been A Snowday...

Mr. O'Brien's back!!

To start class today we tried to graph BY HAND on graph paper these two equations:
a) where the period is π and the amplitude is 1


















b) where the period is 8 and the amplitude is 1















If you are having trouble with graphing, feel free to use the applet http://hotmath.com/util/hm_flash_movie_full.html?movie=/learning_activities/interactivities/translating_scaling.swf. You can also use your TI, Grapher, or Geogebra to check your own work. Personally I really like Geogebra because it's easy to interpret. On quizzes, you'll want to be able to use your TI to help you. Remember to scale the TI graphs by using the "ZTrig" zoom option.

These would be good practice to do if you were absent. The next homework quiz will be on Wednesday, so if you've been having trouble with graphing trignometric functions, tonight and tomorrow night would be a great time to do that.

Remember that for every graph you do in this unit, you'll need to have 5 Key Points. The starting point of sin(x) is (0,0) - for cos(x) it is (0,1). Divide every wave into four equal parts (use π to scale the x-axis if that's more convenient). The starting point and the four points you just made are the 5 Key Points - using these gives you one full period of the graph

The function cos(x) has y-axis symmetry (even) & the function sin(x) has origin symmetry (odd).

The equation to find period change for transformations is . Remember that the equation for any trigonometric function is . You need to know what each of those variables mean and how changes in those variables affect a graph. A good way to change your equation a bit is to factor out the b from the x and h so that you're left with an equation that's easier to understand. This helped us a lot on a).

We discovered a cool identity: . You don't need to know it, but we learned this from playing around with symmetry. Keep symmetry in mind as we look at how graphs relate to each other.

After discussing the warm-up we went over last class' quiz. If you are having trouble with these problems take that as a warning that you probably need to come in for extra help. Don't worry too much if you're having a hard time, but keep working on the things that you're having trouble with. Mr. O'B tries to give partial credit when he can. 15/30 means you're on the right track!
Key Ideas From This Quiz:
* for #3 - to undo a sin you have to do the function on your calculator
* stay in radian mode on your TI!!
* for #5 - Use Pythagorean Theorem
* for #7 - remember to put in the first quadrant in order for both angles to be in SP
* #10 - if you want to get the secant from the tangent just remember that cosine is negative, so secant will also be negative (you're in QIII). Make a right triangle to help you find the other sides

Next we looked at the parent functions we drew last class for notes. If you need to find the graphs for any of the 6 functions you can look on the back cover of the textbook. Also, Nick's last blog post included the graphs of tangent, cotangent, secant, and cosecant. We examined these four graphs very closely and began to understand how they work a little better.
* Tangent & Cotangent: odd. Period = π
* Secant & Cosecant: even.

You don't really need to know the parent function for cosecant - all you have to do is know what sin looks like. To see why this is, you can graph both on one graph and that will illustrate this property to you. Shortcuts are always nice.

If doing trigonometry homework makes you want to cry, check out http://oakroadsystems.com/twt/.

ATTENTION: NEXT CLASS WE WILL BE HAVING CLASS 3A & 3C. EAT LUNCH DURING 3B. Mr. O'Brien will email everyone to remind you. He has ski stuff going on that day. Grazie ragazzi.

Sorry for the long post! Next scribe will be everyone's favorite ginger kid, Lange King (sorry Julia). Homework is on the iCal. Keep asking questions!