Help with inverse funtions (Algebra II)

Hey everybody, if you're struggling with with these inverse functions, here's a good video of some dude explaining them a little bit. Feel free to email me if you have any questions or need extra help. (mrfritz23@gmail.com)

Inverse functions video

Wednesday

Hello all! Today's a great day for outdoor homework! Studies show people think better when they breathe fresh air and are in the sunlight.

Algebra II
In case you wanted to see the solutions to last night's homework, they are here:

4/7 HW Solutions

**Tonight's homework: please print out the "4/8 HW Sheet" and complete it, and bring in your answers tomorrow. If you cannot print them, then rewrite the problems on a separate sheet of paper and work them out on it.

4/8 HW Sheet

- If this word document isn't working for you, try this one: 4/8 HW sheet.pdf

Random Brain Teaser:

A newly married couple recently bought a cottage in a small mountainous village in Vermont. While they were there, the power went out due to a storm, and there was no sign of an early recovery. So they decided to stay at the husband's parent's house until they received power again. Now, the town where the cottage is was so small that the news of the power outage wouldn't be covered in the news, and they were so new to the neighborhood that they didn't have any contacts in the town or even the phone number of the local police department. How then, from the husband's parent's house could they discover when the power was back on in the cottage? (Hint: This brainteaser predates the internet)

Think you know the answer? Leave a comment!

French Fry Friday

It's a good day, a Fri-day!  Free up some time to eat French fries with a friend.

Precalc

Today we reviewed a little of 5.4-5.5 and then took a quiz on said material.  This weekend, bue sure to review for Tuesday's test, and bring questions for Monday!

Notes:

5.5 - Day 2 (From Thursday)

Homework:

Textbook: pp455-456 #'s 4, 6, 19, 23, 24, 32, 34, 35, 40, 47 

Problems not in textbook:

  Suppose A = sin(x) and B = cos(x), and x is in QI.

      Find the following in terms of A & B:

          ex) sin(2x) = 2sin(x)cos(x) = 2AB

      

          1) sin(x/2)     2) cos(2x)     3) sin(3x)-sin(x)

**If you are stuck or want to check over your work, Mr. Hurley has been nice enough to provide solutions for you here.  (For real this time!)

An exciting day for Scientists...

Sometime today around 9AM EST, Dr. Phillip Rosenguard, head of reanimatory bilogical research at Harvard University became the first successful scientist to reanimate a deceased human being.  Some fear that Mary Shelly's depiction of such an event will come true, and this human brought back to life, whom Rosenguard has named Odan (Once Dead, Alive Now) will destroy his maker as well as regular townsfolk.  Dr. Rosenguard assures others though that Odan is a friendly creation, however.  "[Odan] wouldn't hurt a fly, literally.  He's even careful not to step on ants."

Precalc

Today we covered double and half angle identities. (Section 5.5)  Don't forget to consider the quadrant of u/2 when solving you equations!

Notes:

5.4 - Day 2 (In case you were absent yesterday)

5.5 - Day 1

Homework:

HW #3 - p451 #2-26 even; #34-38 even; #46,48

*You all have been working hard, so I thought I'd give you the solutions to tonights homework to make your load a little lighter:  HW 3 Solutions

Spring... brake?

Hopefully this halt in Spring weather will end. I know I want to be outside and experience nature once again!

Precalc:
Today we began our adventure into the world of sums and differences in trig functions. Tomorrow, we begin solving and take section 5.4 a little further!

Notes:
5.4 Day 1 notes

Homework:
p. 440 #1-5; 7-15 odd; 17-26 all

***Due Thursday*** --> Test Corrections Assignment


Algebra II:
Today we discussed solving nth root equations. Tomorrow, we kick it into gear with rational root equations!

Homework:
p4 in your packet

Pot 'o Gold Tuesday

Happy St. Patrick's Day everyone!

Here's a challenge for the day:

Go find a rainbow, and then follow it until you reach the end.  I hear that only on this day each year, a leprechaun hangs out by the northern end waiting for a friend and collecting loose change.  The loose change he turns to gold and throws into his cauldron.  My hat's off to you if you find this mystical creature!

Precalc

Today we covered two lucky charms: general solutions and multiple angle trig equations.  

Notes:

Day 3 notes part 1  (the back page of day 2 notes)

Day 3 notes part 2

Homework:

In your textbook: p432 #11-24 all with gen. sol.'s chicken

Monday... the countdown begins!

Better start buying sunscreen before all of the spring breakers get it off the shelves!  Four days and counting!

Precalc

Today we expanded our love and knowledge of solving trig equations.  We hit calculator expressions, then using identities, and even touched a little on general solutions.  Tomorrow, more 5.3!

Notes:

5.3 Day 2 notes

Homework:

HW #7 --> out #60,65

p431, #5-9 odd (b only); 17-24 all; 32-40 all

Algebra II

Today, we graphed standard form polynomials.  So we factor just like we did in the last unit, and then we use our graphing knowledge that we've learned this unit.  A fusing of units, how clever of those curriculum writers!

Homework:

p13 & p14

Here are a few videos to help with your homework.  It's a couple of the example problems from class today.  

***Be sure to watch part 3 of the first example, I made a mistake that I wanted to clear up.  Can you spot it?

Page 10 example, part 1:     Fullscreen

Part 2:     Fullscreen

Part 3:     Fullscreen

Example 2: Page 11, #2

Part 1:     Fullscreen

Part 2:     Fullscreen

Friday the 13th, version 2.0

Happy Friday the 13th everyone. Be sure to check out one of my favorite Popeye cartoons, "I Don't Scare" for some paraskavedekatriaphobic entertainment. (Look it up!)

Precalc

Today we began our journey into the world of solving trig equations. We took our knowledge of algebra, and our knowledge of trig, and slapped them together to make a nice trigebra sangwich.

Notes:

5.3 Day 1 notes

Homework:

HW #6 -> p431 #6-10 (even, a only); 12-16 even (in the interval [0, 2pi) ), #26-31 all, 42-50 even

***don't do 2 or 4!

Algebra II

Pi Day!!!

Homework:

watch the popeye video!

and have a good weekend!

Thankful Thursday

Today, I'm thankful for students. They bring me much joy.

Precalc
Today we worked more on verifying identities. Tomorrow, we'll plunge into equations!

Notes:
5.2 notes - day 1 & day 2

Homework:
All multiples of 7 up to 140 in the trig identities packet

*Hint: for #140, you will need to substitute a pythagorean identity immediately twice on the left-hand-side of the equation. Then consider the LHS as a quadratic and go from there

*Hint 2 for #140: After some reworking, you may want to use a conjugate (on both sides). From there, maybe you can split fractions and rewrite in terms on sines and cosines...



Algebra II
Today we reviewed some of yesterday's material and worked on more graphing. It was awesome. Tomorrw, we'll kick it up a notch, so get juiced.

Homework:
In your packet - p8 #'s 1,3,4 on the bottom

Torrential Tuesday

Isn't it interesting to think that here in the Chicago area, we've been getting more rain than we know what to do with, and at the same time, there are areas in the world that haven't had rain in months? If only we could teleport rain clouds...

Precalc
Today we completed the last of our three-day coverage of simplifying trigonometric expressions. Good job everyone, we made it! Tomorrow, we use these skills and dive into verifying trig identies - where it gets even MORE fun! If you are feeling like you're not getting the hang of this, please come and see me and I will help you and show you more examples. A solid understanding of this material is crucial!

Homework:

worksheet #3 - ALL


Algebra II
No homework! Go jump in some puddles and play in the rain!

The Sleepiest Monday of the Semester (...so far)

Hello everyone, happy daylight savings time! Waking up an hour earlier can be a bit rough, BUT we can now have outdoor fun one whole hour later than we did last week! I don't know about you, but I will be tossing a frisbee around for sure today.

Precalc

Today was another exciting day of simplifying trig expressions, or what I like to call "math magic." Be sure to stay sharp on your simplifying strategies, as they will be used even more tomorrow!

Notes:

same as Friday, with some new notes towards the bottom

5.1 notes - day 2

Homework:

Worksheet 2 (just the odds)

Algebra II

Reharsal test today. Be sure to study for the real deal tomorrow. Also, don't forget tomorrow is your last day to make up power quizzes!

Be sure to check your answers on the practice test, and feel free to email me with questions (mrfritz23@gmail.com)

Practice test answers

Also, here's a little tutorial on how to use graphing calculators to graph functions:

tutorial

(on the bottom of the screen is a "show me" link that actually shows you with a calculator how to graph these functions.)

Friday March 6th - "Everybody's workin' for the weekend!"

Hello everyone! Today is a beautiful day; it's perfect weather for some outdoor math appreciatiation. Try doing your homework outside for an extra boost in your mood.

Precalc

Today we started the ever-exciting chapter 5! Don't forget those strategies we talked about in class... you better RECKONIZE!

Notes:

5.1 notes - day 1

Homework:

worksheet 1

Algebra II

Review, review, review. Don't forget on Monday is the practice test, and on Tuesday is the REAL DEAL. Let me know if you need any review problems or help on any of these topics.

Homework:

The rest of page 46 in your packet

March 4th, 2009

Precalc

TEST TOMORROW!!!
- Best of Chapter 4! Hurray!
Here's a review guide for you to study with:

test review


Algebra II

Now we can use graphs to narrow down our choices of Possible Rational Roots! This makes life much easier, resulting in sounder slumbers.

Homework:

p36A & p36B -> ALL

March 2nd, 2009

Precalc:

Today we discussed the definition of the arcsin(x), arccos(x), and arctan(x) functions. Be sure to get comfortable with all of their domains, and ranges. Also memorize your UNIT CIRCLE values!!!

Notes:

For a copy of the notes from today, click here.

Homework:

#4 on the schedule: p384 #5-14, 33-41 odd



Algebra II

Today, we embarked on a journey and came upon the rational root (zero) theorem. In case you missed the definition:

RRT - all of the possibile rational roots of a polynomial can be found by dividing ALL of the factors of the constant term by ALL of the factors of the leading coefficient.

Homework:
pMP3 - all
pMP6 - 1-3

If you're having trouble, here's an example problem with two parts... Enjoy!

Part 1:
fullscreen here


Part 2:
fullscreen here

February 26, 2009

Precalc:
Today we worked on an activity to discover how to write equations of given secant, cosecant, tangent, and cotangent functions. To download a blank copy of this worksheet, click here.

To download a competed version with correct answers, click here.

Download the completed version and then compare it with your sheet. Are there any differences? What caused these differences? Are they necessarily wrong?

Homework tonight:

Worksheet 2

Algebra II:

Double Synthetic Division!!!

Don't get too discouraged, remember, all you're doing is synthetic division twice. Break up your polynomial into factors one by one. And ~ don't forget check if quotients that are quadratics are factorable!!!

Homework:
p 30 - all questions under III (1-3)

Feb. 25th - 3 days of February left...

Did you know...?
On this day in 1943 Beatles guitarist George Harrison was born in Liverpool, England.
and...
In 1964 Cassius Clay (who later changed his name to Muhammad Ali) became the world heavyweight boxing champion by defeating Sonny Liston in Miami Beach.

Precalc:
Today we talked about the cotangent function and how it relates to the tangent function.

Homework:
Worksheet 1 (will be added soon)

Algebra II:
Today we went over synthetic division and the definition of "zeros." For those of you who forget, a zero is solution for 'x' that will make a polynomial equal to zero.

Ex: -2 is a zero for the polynomial x^2 + 5x + 6 because if you substitute -2 in for x, the polynomial equals zero, which also means that (x + 2) is a factor of this polynomial.

For help with synthetic division (and long division) the powerpoint used in class is available for download here.

Feb 24th - Mardi Gras!

Precalc :

Today we covered the graph y = atan(bx - c) + d

Homework is on the schedule --> #2

notes:  4.6 day 2.

Long division of polynomials

Here's a gift for you all:
The solution to problem 8! Fullscreen here


Here's a sample long division problem on p26. The first video is how to find the solution, and the second is how to check it.

Fullscreen


Fullscreen

Sample problem using tons of tools

I think this problem, or one similar to it, was on that factor frenzy sheet we did last week. Here are two different ways of approaching the problem, the first starts with the difference of squares, and the second starts with the difference of cubes.

Video 1:
fullscreen here


Video 2:
fullscreen here

Factoring using diff. of squares

Here's another video..
fullscreen here