
Monday, June 16, 2014
Goodbye for now!

Friday, June 13, 2014
Dev Katherine Marissa
Thursday, June 12, 2014
DEV Project
Sin(x)(cos(x)+1)/cos(x)=(sin(x)*csc(x))(tan(x)+sin(x))
-First, distribute sin(x) to cos(x)+1.
(cos(x)*sin(x)+sin(x))/cos(x)=((x)*csc(x))(tan(x)+(x))
-Separate the addition being done to (Cos(x)*Sin(x)+Sin(x))/Cos(x).
(Cos(x)Sin(x))/Cos(x)+Sin(x))/Cos(x)=(Sin(x)*Csc(x))*(Tan(x)+Sin(x))
-Then multiply (Sin(x)*Csc(x)) together and see that they multiply to equal 1.
(Cos(x)Sin(x))/Cos(x))+(Sin(x)/Cos(x))=Tan(x)+Sin(x)
- In the (Cos(x)Sin(x))/Cos(x))+(Sin(x)/Cos(x)) section, have the first cosines divide out.
Sin(x)+(Sin(x)/Cos(x))=Tan(x)+Sin(x)
-Turn the (Sin(x)/Cos(x)) into Tan(x).
Sin(x)+Tan(x)=Tan(x)+Sin(x).
2.The time on an analog clock is 7:54. Find the angle made from the minute hand, clockwise to the hour hand.
-From the 11 to the 7th hour on the clock there are 8 ∏/6 's, which is just 8∏/6.
-From the minute hand to the 11 there is 1/5th of a cycle. To turn the 1/5 into radians you have to multiply it by ∏/6 to get ∏/30.
-From the hour hand to the 7 there are 9/10ths of a cycle and when multiplied by ∏/6 it equals 9∏/60.
-To get the total distance between the minute hand, clockwise to the hour hand we need to add all of these distances together which would be (8∏/6)+(2∏/60)+(9∏/60)= 91∏/60
-91∏/60 is the final answer.
3. Convert 76∏/12 to degrees and find its co-terminal angles.
In order to first convert this angle to degrees, multiply it by 180/∏ since there are 180 degrees in 1∏.
(76∏/12)*(180/∏)
The pies make a 1, and you can instead multiply 76*15 to make it easier since 180/12=15.
76*15=1140 degrees.
Now that we have converted the radian measure to degrees, we now will find the coterminal angles of this measure on the unit circle. Since there are 360 degrees in the unit circle, we both add and subtract 360 from 1140 to find the angles that are the same on the unit circle, but have different degrees
because they are in different cycles.
1140+360=1500 degrees
1140-360=780 degrees
You have now found two coterminal angles of 1140 degrees.
4. The highest point of a ferris wheel is 471 feet off of the ground. The loading point is 13 feet off of the ground. It takes 3 minutes and 30 seconds to make one revolution. Find an equation that represents height as a function of time in seconds.
In order to write the equation, we will need to find the amplitude, the vertical shift, and the b value.
To find the amplitude/wavelength, we need to take how high the bottom of the ferris wheel is off the ground and subract it from the highest point of the ferris wheel.
471-13=457 ft.
This will give us the height of the ferris wheel. Then, since the amplitude is half the height of the ferris wheel, we divide the height of the ferris wheel by 2.
457/2=228.5 ft.
amplitude=228.5 ft.
Now we need to find the vertical shift, which is how high the point of origin is off of the ground. Since the origin is half of the ferris wheel added to how high the bottom of the ferris wheel is off the ground, we will just plug in the numbers.
amplitude/half of ferris wheel: 228.5 ft.
height of bottom of ferris wheel off the ground/ loading point: 123 ft.
228.5+123=241.5ft
vertical shift/k value= 241.5 ft.
Finally, we need to find the b value. The equation to find the b value is 2∏/period, and the period in this case is 3 minutes and 30 seconds, which is the time of one revolution. First, we need to convert minutes into seconds.
3 minutes and 30 seconds= 210 seconds
2∏/ 210= ∏/105
Now that we have all of the necessary components, it's time to write the equation that represents height as a function of time.
y=aCos(b+h)+k
Now, just plug in the numbers.
y=241.5-228.5Cos∏/105t
5. Find the tan(105 degrees)
First, you have to find the individual tangents of two known angles on the unit circle that add to 105. For this problem, 60+45 is the easiest way. Use the tangent addition identity equation and plug in the numbers.
tan(60+45)= (tan60+tan45)/(1-tan60*tan45)
Next, replace the tan60 and tan45 with the actual values, calculated using Y/X.
tan(60+45)= (√3+1)/(1-√3*1)
Then, rationalize the denominator by using the special form of 1.
=(√3+1)/(1-√3)*(1+√3)/(1+√3)
=(3+1+2√3)/(1-3)
After that, finish solving the equation.
=(4+2√3)/(-2)
We can factor out a 2 in the numerator, since 2 goes into both 4 and 2√3.
= 2(2+√3)/(-2)
The 2's then divide out, leaving a negative 1 in the numerator. This gives us the final answer of:
-(2+√3)
6. Simplify the identity.
sec^5(x)+1/(cosx+sin^24x)+5/(cos^2x)
=1/(cos^5x)+1/(cosx+sin^24x)+5/(cos^2x)
So the new equation is:
(cosx+sin^24x)(cos^2x)/(cos^5x)(cosx+sin^24x)(cos^2x) + (cos^2x)(cos^5x)/(cos^5x)(cosx+sin^24x)(cos^2x) + 5(cos^x+sin^24x)(cos^5x)/(cos^5x)(cosx+sin^24x)(cos^2x)
Super messy, but now we can add the numerators together. But, before this, we have to distribute the terms in the numerators to each other to get the terms outside of the parentheses.
(cosx+sin^24x)(cos^2x) = cos^3x+sin^24x*cosx
(cos^2x)(cos^5x) = cos^7x
5(cosx+sin^24x)=(5cosx+5sin^24x)(cos^3x)=5cos^4x+5sin^24x*cos^3x
So, now we have terms to add together without parentheses.
(cos^3x+sin^24x+cosx+cos^7x+5cos^4x+5sin^24x*cos^3x)/(cos^5x)(cosx+sin^24x)(cos^2x)
Notice there are both (cos^2x) and (cos^5x) in the denominator, which can be combined to become (cos^7x).
This new (cos^7x) can be divided with the (cos^3x) in the numerator, becoming (cos^4x) in the
denominator, since both are being multiplied.
So, the final simplified equation becomes: (really messy, but about as far as you could easily go)
(cos^3x+sin^24x+cosx+cos^7x+5cos^4x+5sin^24x)/(cos^4x)(cosx+sin^24x)
Ryan's reflection: We chose these problems for the D.E.V. project because we believe they best represent the units we've learned this trimester. We chose a few problems, such as #6 and the ferris wheel to challenge ourselves and to really see how well we understood everything. I think that working through these problems with Tyler and Edmund made me understand the content more than ever before. It helped with prep for the exam and my future calculus endeavors. We tried to use problems that were a little bit of everything from the trimester. Not only will it help me with math related problems in the future, it also helps to gain experience working through problems with a group of people, which is almost guaranteed to happen sometime in life. What I learned is that even when you challenge yourself and the problems seem impossible, time is the most valuable resource. If you take time to work through extremely difficult problems, you can achieve the correct answer. This was my 2nd DEV and overall another great experience for me.
Tyler's reflection: Creating problems for the D.E.V. project has made me look back at earlier tests and homework assignments, giving me a chance to look back at how to do certain problems to get me ready for the upcoming exam. When working through some of the identity problems, I had to figure out how to start from the end and change it into the beginning of the problem which helped me figure out different ways to verify identities.We chose these problems because it took a little section out of every unit we worked with this trimester and used problems that accurately represented our knowledge of these units.These problems accurately provide an overview of my best mathematical understanding of what I've learned so far by how complex we tried to make them while still being able to work with. What I learned from this project is that i knew more about these units than i really
thought and that this will really help my understanding when I go to take the exam.
Edmunds reflection: Our entire group learned a lot from this trimester's dev project. We came up with problems from all three units we have learned, and made sure the problems we picked reflected the main ideas of each unit. For example, we did a convert radians to degrees problem as well as a clock problem. We did these problems because the conversion helps you to better understand the unit circle while the clock problem requires previous understanding of the unit circle to complete. One of the problems we took from unit 2 was a Ferris wheel problem, because in order to write the equation you would need to have an understanding of trigonometric equations. We picked a verifying identity problem for unit three because it combined all previous problems we had to solve in that unit. I learned a lot from this project, because this tri I attempted to explain the problems like I was actually teaching, as opposed to just writing out steps. My mathematical understanding of many concepts improved because of this project.
DEV
here's my DEV
overall i had a lot of fun filming the DEV... i had to use Openshot while running Ubuntu, a Linux os, which is a tremendous pain. but i learned how to get it done. i believe the most important things we go over in class is the basics. if you don't have a clear understanding of the basics, you can't move forward. in my video i go over 4 aspects of the class and 1 use of the material. initially i had difficulties with getting the basics because of my adhd, however if i hear it multiple times and quickly i can understand it very well.
Wednesday, June 11, 2014
Christian's DEV project
Kristin's DEV
I chose this problem set because I felt they were the types of problems I had the best grasp on. But trying to make them all story problems AND make the problems themselves challenging proved to be really hard for me. I learned that being a math teacher sucks, but I also learned a few new things about taking care of infants, thanks to the theme of my DEV. Also my wifi has been particularly slow today and it's a little infuriating to have a bad connection while you're trying to upload a 35-slide power point onto dropbox so you can get your project so you can study for your exam that you have in the morning. Bright side! I'm pretty much done being a Junior. That's amazing.
Here's the link for my project:
https://www.dropbox.com/s/xtr7el9r52gme93/THE%20Daddy%20DEV%21.pptx
DEV Project: Kaitlyn K and Rhiannon
Rhiannon's reflection:
DEV project by Ally and James
James: This class seemed to be easier than functions last trimester. The DEV project was easy to think up ideas with the graphing and the identities to chase from. The graphing and the identities were the easier part of the class to remember compared to remember the entire unit circle with all of the radians and the degrees. The unit circle would have been easy to write up but the steps to make it would take a couple days to type up and find a unit circle to use for the DEV project.
Ally: I decided to choose these units because at first they were difficult for me. I was so used to using a calculator and adding, subtracting, multiplying, and dividing radians was something I wasn't used to without a calculator. towards the end of the units it got very easy for me to be able to do this. I also choose these units because it reminded me of what I did in Algebra 2b, and I was very familiar with the unit circle and still have it memorized since that class. This DEV project has expanded and enhanced my knowledge on the Trig. identities and proving those, and graphing and figuring out my own way to make graphs and there inverse functions as well. This class has challenged me with the idea that you don't need to rely on a calculator, and that the brain can do a lot more than what you even think. I'm very glad I took this class and I hope to continue on in math pass this year.
DEV Project Lauren and Lindsey
Tuesday, June 10, 2014
D.E.V. Project - Gavin
I found that actually making the problems definitely proved to be the hardest part of doing this project as it was tiring to try and find a happy medium between complexity and simplicity whilst covering the required topics without making too boring at the same time (Not that it's really exciting either!). It was a good learning experience for the unites and problems I did though, sicne it required me to do much more than just solve it on a piece of paper as I really had to know how it worked to make a decent video of it. Oh Before I Forget, make sure you don't make yourself too busy all the time and actually work on the project gradually as I came up with a lot of the stuff yesterday and then did all the recording and editing today like an idiot.. Don't be like me!
On a side note I wish I had better lighting as I couldn't find any fixtures that would have worked right and it's much too dark during the video.. (Dem shadows..).. Also that video editing was awful I mean wow.. GG Gavin.. Anyways lots of fun!
My D.E.V.
I noticed that when I went through my prezi sometimes the videos had issues and only displayed a green screen instead of what I filmed. Usually restarting the presentation where I left off fixed it, but here are the links just in case!
Problem 1: PART 1
Step 1: https://www.youtube.com/watch?v=RCCVJH-J-VU
https://www.youtube.com/watch?v=fElKtI-Zydc
https://www.youtube.com/watch?v=7-5Yc-wUMeU
Step 2: https://www.youtube.com/watch?v=_HJYejX9cGk
Steps 3&4: https://www.youtube.com/watch?v=H81vMLJoGa0
Step 5: https://www.youtube.com/watch?v=PizFYDCWbUM
Step 6: https://www.youtube.com/watch?v=G0QO8SO5D6c
PART 2: https://www.youtube.com/watch?v=OhOIGJWgI5E
PART 3: https://www.youtube.com/watch?v=jzSXz67yCT8
Problem 2: https://www.youtube.com/watch?v=KtY3Nsl9wFo
https://www.youtube.com/watch?v=GhZ3j_v9lKU
Problem 3: https://www.youtube.com/watch?v=4A2Ru_hJXHE
https://www.youtube.com/watch?v=6akQFG5-CZc
https://www.youtube.com/watch?v=DyGxwCwqdjU
Problem 4: https://www.youtube.com/watch?v=R1D5GhueD00
Monday, June 9, 2014
DEV
Reflection:
I chose the concepts I did because I understood them enough that I thought I would be able to explain them. I'm not all that great at math, and I wouldn't consider myself an expert at it at all. I actually took my time on this and tried to do the best I could.This assignment did help, because it made me feel more confident about some of the things we did earlier this trimester for the exam.
Saturday, June 7, 2014
Wednesday, June 4, 2014
MAkeup Blog post- my journey in pre-calc trigonometry
. This is the work I had, and the work that I recently just did. I now understand how to get it to radians. One thing I do need to still practtice is converting that to degrees.
But overall, I have been working hard to understand this material. To any future trig student I really suggest being very studious in this class because it will pay off in the long run. I have really enjoyed Trig.
Sunday, June 1, 2014
B.O.B. Week 8
B. O. B.
Thursday, May 29, 2014
Gwens DEV
Reflection: I think this project was a really good challenge for me in that I had to both explain and create problems for "others". I was challenged because I have overall had a fairly difficult time understanding the content of this course in general. I chose the two problems I did because they seemed like a big challenge to me (being that I have a hard time with the content in general) but not so much so that they were impossible. I enjoyed thinking about the problems from the "other end" when I was creating them because that gave me a unique perspective of what the problems really entail. When I created the problems I got to see all that goes into a problem like this and gain a deeper understanding of the content as a whole. I chose to do the first problem about the travel to Vienna via Seattle for two reasons. First because it is a good problem that provides a good example of an application of what we learned in the first "Unit Circle" unit. Secondly I chose this problem because then I would be able to include a "travel theme" to my DEV project. I specifically chose Vienna and Seattle because that is relate-able actually will be flying out of Seattle (where my travel agent actually is) to Vienna for a year. I thought this problem would be especially cool because I could find out how far it actually is to Vienna and apply what I learned in Trig to do it. I chose the Ferris Wheel problem sticking with the "travel theme" and also because I really did struggle with the ferris wheel problem the first time we did one, and thought that some extra practice would be very good. I chose the London Eye because it is one of the most well known Ferris Wheels in the world, and is a place I will travel next year. This problem provided a challenge to me because I had no indication whether or no my work was right, and had to trust all of the knowledge I learned in class. I was particularly challenged by this problem because the outputs changed so much, into number that were so different that the typical 0, pi/2, pi, 3pi/2, 2pi. This challenged me to really work and check my work in more ways than usual. Overall I feel like this project was a great challenge for me and helped me prepare for the exam a lot because I had to include problems that encompassed two units and apply them at a higher level than usual. One thing that helped me with this project was that I did not really understand the content much at one point, so I tried to make my explanations simple so that the reader could understand how to do the problem and as my explanations became more complicated would be able to apply their knowledge to a higher level as well.
BOB
Tuesday, May 27, 2014
Ben Anderson's Dev. Project!!!
https://docs.google.com/presentation/d/1pZYhiClpU2BDiwNwo0--pqzYju3GJLUw0EwM1td-nWk/edit?pli=1#slide=id.p
I also have links in my google presentation that everyone has access to as well!!!
Yeah last B.O.B.
Monday, May 26, 2014
last BOB
The Last BOB of the school year
Bob
last blog post...thank god
Sunday, May 25, 2014
Last BOB
Ahhhh!!!!! This tri has gone by so fast!!! But this has been such a great year... sure it had some downs but overall I'd say this year has been pretty good...
So this new stuff... getting the hang of it, substitution and algebra. Seeing how all of this connects together is interesting and dare I say mind blowing!!!
term reflection
L.B.O.B.
B.O.B. Week 7
BOB
Bob 6
B.O.B. - Reflection of last week
BOB
One struggle for me was keeping up with the homework check. It seemed like it took me five-ever to finish everything and I couldn't bring myself to understand two of the problems until the day before the test when I was there after school.
I also feel conflicted about our test. I felt okay about it, but I get the sense that I didn't focus enough while I took it and I may have messed a lot of it up. With that said, I have strong reservations about having confidence in it. I just can't wait to get it back so maybe I can do test corrections.
I think I like what we started after day two of the test. I was having trouble focusing on it at first but I liked it by the end. Unfortunately...I missed Friday for the Cedar Point trip (which was SO fun! *shout out to Derek T and Kristen R #workhardplayhard) and I don't know if I'll be able to easily catch up.
Overall, I think I'm just tired. I don't sleep enough and I can't focus in class which makes me only half understand things and fall behind. I think I'll try harder at that this week.
~A very sleepy Katie
Goodnight :)
B.O.B
B.o.b.
Identities
BOB
BOB
Last B.O.B!
A reflection on a particular day.
On Friday, we started to learn more about the Pythagorean identies involving writing "in terms of" expressions for sin, cos, tangent, secant or cosecant. I am starting to get the hang of it, but some problems are a little tricky because there isnt an equation for some identities! We also got time to work on our D.E.V project which I really enjoyed because I havent had time to really sit down and work on it. Overall it was a very progressive day. This year has gone by sooo fast!
Bob
Final B.O.B.
final B.O.B Post
Bob
blog
Creative BOB Tilte
BOB
B.O.B. Reflection
B.O.B. #6 Reflection
Saturday, May 24, 2014
My blog
B.O.B reflection
Friday, May 23, 2014
BOB
B. O. B.
BOB problems
Thursday, May 22, 2014
B.O.B.
Wednesday, May 21, 2014
Test day
Monday, May 19, 2014
BOB-late from last week
~Katie H :)
BOB
Bob
BOB muddiest point
Sunday, May 18, 2014
BOB
BOB
BOB
BOB
B.O.B 5
B.O.B. Week 5
B.O.B. 5
thinking about my day
B.O.B. Week 6 (?)
B.O.B. Refelction
B.O.B. Reflection
Bob 5
B.O.B- Muddy Point
B.O.B #?
So this past week hasn't been too bad. I had a lot of stress cause of the AP world exam and, was distracted from any other subject. I'm a bit shaky on graphing tangent waves, they have lots of different rules and cotangent is confusing as well. I'll figure it out by Wednesday because writing equations for them is making more sense rather than graphing them alone.
Ready or nah?
B.O.B.
BOB
BOB #(I lost count... 5/18/14)
B.O.B. Reflection of last week
Everybody: catch up on sleep from last night and start happy in the week with the memories from prom:)
B.O.B Number Something
B.O.B
A reflection on my progress.
This unit on graphing and writing eqauations for sin, cos has been pretty easy to me. I like it alot and it seems im always done with whatever packet we are assigned early! Also, for just learning how to graph the secant, cosecant and tangent I think I am doing preettty well. I really enjoy this unit alot and its nice to understand something completely in Precalc Trig! So, overall I believe my progress is making a steady incline from not so good to good!.
Progress so far
Week reflection bob 6?
Saturday, May 17, 2014
Creative BOB Title
BOB class reflection
Friday, May 16, 2014
Blog post
B.O.B. 5# Reflection
Thursday, May 15, 2014
BOB
B.O.B. How I Feel About This Class
Monday, May 12, 2014
B.O.B. 4
^ + --> = Carretero
BOB
Sunday, May 11, 2014
BOB
B.O.B
This ferris wheel project is a challenge. There's a lot of work to be put into it but I'm sure my group and I will get it. I feel like once we start on one part of the project then the other steps will show up and we'll be able to solve them, kind of like dominoes
BOB
A Specific Day in Class
Muddiest Point
Bob
BOB 5
B.O.B reflection
B.O.B. Week 5
Bob 5?
BOB - Reflection
B.O.B.- Reflection
B.O.B.
My progress this week
B.O.B. 4
Muddy Point
BOB A Real Life Example
B.O.B. Reflection on the week
Saturday, May 10, 2014
B.O.B.
B.O.B. - Relate math to real life
My B.O.B
Bob 4
B.O.B. Reflection 4#
Friday, May 9, 2014
BOB for the week that it is currently
B.O.B.
B.O.B. Gangstaaaaa
BOB
P.S. Thanks for being such a great teacher, Jackson :) And I'm super excited for you with baby Clark coming so soon!
BOB
Thursday, May 8, 2014
B.O.B
On one of my earlier blog posts i have done a reflection of the week instead of one particular day. So that is what i am going to post about again.
This week, through Monday, Tuesday,And Wednesday, we have been working on graphing and writing equations for cosine and sin functions. I find this to be pretty easy and my most favorite unit so far. Out of graphing and writing cosine and sin equations, i would say i like graphing the most. When graphing a sin or cosine function, i like to solve for the horizontal and vertical shift. I like a challenge, and graphing and figuring out where the shifts happen is really fun in an odd way. Futhermore,on Thursday(today) we went over applications for sin and cosine. We also took a 4 question quiz and got to use our notes! This week has been a good week!