Have a great summer!  I'll be here if you need anything!

Jackson

D.E.V. - Tyler Guy & Aaron Gregory

This is the D.E.V. Project for both Tyler Guy and myself (Aaron Gregory). The project reflections are at the end of the video.

D.E.V.

well here's my D.E.V.

Savannah And Corie's DEV

Zombies

 (all photos from google.com/images & tumblr.com)


Corie's Reflection: This is the second DEV project that I've done, and I found this one to be a lot simpler. Same amount of problems and same basic way of showing it, but since I had figured out prior to doing this how to put it together, it cut my work time down a lot! But still these were some difficult problems to come up with, and I came up with about fifteenth problems total for this project just because I wanted options. I feel as if this project helped me understand these units more and I really enjoyed applying one of my favorite t.v. shows to a school project. Although I would never want to do another DEV project, ever.

Savannah's Reflection:  Out of the two DEV projects I've done this one seems to be a lot easier than the other one. For this project we did the problems before hand instead of doing them the dame day we worked on the power point which made things much easier in the long run.  Some of the problems we did where ones that we ourselves had trouble with or that the whole class had troubles with.  This project always seems to help me understand some of them problems a little better and helps me when i get to the exam as well because we spent so long figuring them out that it stuck in my brain.  This project was a success like that last one.  

D.E.V. By: Paige Miller and Nick Hudgins

This project was just as much work from the first time. I loved doing it yet again. Only this time I had a partner. Which was awesome. It helped me so much. Because we did problems that I was having trouble with. I like doing this project it helps a lot. Especially studying for the exam. -Paige Miller

I have never done a project like this. It was new to me. Yes it was a lot of work don't get me wrong but I loved doing it. We did a whole bunch of different kind of problems. I loved creating them! I hope you enjoy! This theme is one of my favorite TV shows. -Nick Hudgins

https://www.dropbox.com/sh/yfqp614htyjmd48/9N4y7xGlAI?m

Paige-Dev

My reflection: I chose problems and concepts 

that I feel I best understand. Problems I believr I could assist others with. To be quite honest there is much about this class I do not fully understand. So I worked with what I had. What I learned while creating this project os little more about why I get the answers that I do rather than just getting some odd number and rolling with it.  I struggled slightly because of the lack of structure in this DEV. I guess I found I work best with more guidelines or rules. Although I do thoroughly enjoy the creative freedom.

D.E.V.

Unit 1 - Measurement

Find the exact value of each trigonomic function.

The first step is to get csc θ by itself:

-8 –8csc θ = -24

Add 8 to both sides of the equal sign

-8csc θ = -16

Divide both sides by -8

 csc θ = 2

Change to sine

1/sin θ =2

Move sine to numerator

sin θ = ½

Look on unit circle to see where sin is ½

Θ = π/6 , 5π/6

Unit 2 – Graphing

To describe a transformation, you will first need to understand the different variables of a graph and what they do.

The formula:

          y = a * cosb ( θ – h) +k

a = rate/amplitude                                      h = horizontal shift

b = horizontal stretch/shrink             k = vertical shift

When given the problem:     y = 4sin (θ - 3π/2) + 6

The 4 is your “a” value, therefore, the amplitude is 4.

There is a right shift of 3π/4

The graph shifts up 6

All of this can be determined from looking at the equation and matching up the variables.

Unit 3 – Identities

Problem: cosθ/secθ + sinθ/cscθ

First, convert everything into sine and cosine.

= cosθ/(1/cosθ) + sinθ/ (1/sinθ)

= cos²θ + sin²θ

= 1

The answer 1 can be found from looking at the Pythagorean Identities.

Unit 4 – Inverses

Problem: sin(cos^-1  (√3)/2)

First, find the cosine, and use that to fine the sine.

= sin(π/6)

Then, look for the sin of π/6 on the Unit Circle.

Answer: ½

I chose to do a problem from each unit because this way, everything is covered for my personal review. I really wanted to focus on the basics because I have been struggling in this class. I feel like going through the basics has actually helped me a lot more in understanding where I have made so many mistakes. Overall, I was able to understand what was going on and the project was very eye opening. When working on it by yourself, you really get a chance to see where you struggle and need to work harder at. I saw this as a very beneficial way to review because you were able to tackle what you needed to. I’m hoping that I will do a lot better on the exam than I have been on quizzes and tests.  

Doug and Nathan DEV

https://www.dropbox.com/sh/pv6ga8i8zoyvrqo/aBxgS6gx3-/DEV%20trig.pptx
 Our reflection are the last two slides

Nathan and Doug

DEV (Alli Hope and Abbey Soule)

click!

The Last B.O.B. of the Year (Interesting Point)

What I found really interesting is the arcsine or the inverse of sine is not the same as sine to the -1 power.  I had used arcsine several times in my past homeschooling to solve for angles and I didn't find it very difficult but I had always just assumed it was the same as sine to the -1 power and I found it very surprising to be otherwise.

My final B.O.B. - Jacob Evenson

<post>

Well, this is a rather impromptu B.O.B. because I just noticed a twitter update on the right warning of a blog post due tonight.  So, here it is!

This has been a rather interesting school year for me.  Unfortunately, much of it has been a blur throughout this last Trimester.  For the past month or so, I've been completely flooded with homework, working for 6+ hours every night, preparing for my Civics hearing, or practicing for an oral exam in Spanish class, or working on the DEV, or studying for the weekly Physics quizzes.  Though I must say, we have not received nearly as much homework in this class as I had expected.  I remember getting TONS from Functions, but I was surprised at the relatively low workload generated from this class.
Especially from that last unit!  We hardly had to do anything, and had tons of time to work on it in class.  I didn't find it especially difficult, the only problems that I even slightly struggled with were things like sin^-1(cos(x)+sin(x)).  But I asked for help, and got that all squared away.

</post>

D.E.V. Project

I wanted to do a shout out to my partners.  They were great and I enjoyed their ideas and input.
http://funprecalctrig.weebly.com/

D.E.V. Allie R., Aaron R., Erin B.

Our reflections are on the website.

http://the3asprecalctrig.weebly.com/

D.E.V.

https://plus.google.com/u/0/102516641088293549905#102516641088293549905/videos
Above is the link to our project! when you click on the link scroll to the top of the page and click on youtube. The videos will be there.

This project was one of the more fun projects Grant and I have ever done. We had a lot of freedom and could pretty much do any problems that we wanted. There were no real reasons why we picked the problems we did. We just tried to very them and make sure we gone in problems from all of the units. We feel like the problems we choose showed both of our strenghts. Grant is very strong with graph problems as well as solving equations. Josh is strong in finding the exact values of degrees and he is also good at solving. Overall we thought this project was very educational. It gave students a lot of freedom and this is good. In college the professor won't be there with you every step of the way and you have to do things on your own. This project we feel is much like one you can find in college and it is good that we have been exposed to this.  

I am very sorry Mr. Jackson but for some reason when the videos were up loaded to youtube they got flipped upside down. I tried to flip them but I dont know how. I hope this wont affect our grade very much.

Thanks,
Grant and Josh

DEV project

Problem 1)

Suppose a Ferris wheel has a 15 ft tall ramp and the diameter of the wheel is 80 ft tall. It makes a complete revolution in 20 sec. Write a mathematical equation that describes a relationship between the height of the rider above the bottom of the Ferris wheel and time.



First, we set the period of  20 seconds equal to 2pi/b, then we determined the b value to be pi/10. we knew our amplitude was -40 because the rider boarded on the bottom of the wheel and the diameter is 80. the vertical shift was +44 because the amplitude plus the height of the ramp equals 44. The equation was cosine because it started at the bottom of the Ferris wheel.

Problem 2)

Richar Ressler, a famous astronaut, came up with the idea that the brightness of a moon increases and decreases with itself. the moons radius is 1000 miles and changes by 1 mile a day with each flash of light. if the time between periods of maximum brightness is 3 days have an equation that describes the radius o this moon as a function of time.

We set the period of 3 to pi/2 and got our b value of 2pi/3. The vertical shift was 1000 because that is the radius of the moon. We knew the sine graph would increase and decrease a 1 mile both ways because that is how much each flash of light changes.

Problem 3)

using our identity formulas, we knew that the right side of the problem was equal to 1. The top of the right formula cancelled out to one and the bottom of the equation was an identity that equaled one. So each side of the equation equals 1.

Problem 4)

 We worked on the top of the left side first and got it sin^2X times cos^2X. We put that over the bottom half of the left side, which we got down to 1/sin. to get rid of the fraction underneath a fraction, we had to multiply the reciprocal of the bottom times the top. The left side came to equal sin^2X times cos^2X and same with the right side of the equation.

Problem 5)

The top side of the left has an identity equal to one, so the top part of the fraction is now "cot^2X + 1" which equals csc^2X. After we put that over the bottom part of the fraction it became csc^2X over tan^2X. we then multiplied the reciprocal and the left side became cos^2X/sin^4X. The right side of the problem was cos^2X/sin^2X times 1/sin^2X. Both sides then equaled cos^2X/sin^4X.

-P.S. we worked really hard on this amazing project, Jackson.



lexi: 

This project was kinda fun to me once we started to do it. iIt took alot of time and effort but i do not think it was too hard! me and richar both worked equally through it so not too much work was put on just one of us.



richar: 

i did not really like this project, we had to put in a lot of hours but i think it turned out good! i really hope we get a good grade on it though because we need it to help our grades and that would be awesome!

Derek, Shaun and Dillon's Dev project 

A link to our prezi http://prezi.com/lidyn3lvsjp6/pcalc-trig-dev-project/

Shaun's Conclusion 

For my Dev project I Worked with Dillon and Derek. I chose a solving identity problem because it was a challenging concept for me at first but after I understood it, it was very easy for me. For my first solving identity I picked one that was way over the top which I ended up getting stuck on and couldn’t make any progress so changed it so it would be a bit easier and not have so many fractions. For my second problem I chose a problem that we sketched a triangle for so that we could find the values to plug into another expression. Overall I think this Dev project was easier then the last one because my two problems were not graphing problems. I think that this was a good way for me to remember all of the things we have done over this trimester because I kept looking back through old tests and packets to figure out how to do some of the problems. 

Derek's Conclusion

For the Dev project I worked with Shaun and Dillon. I feel this Project has provided a good review right before the exam. This project has also taught me communication is key. I feel this project was a good way to end the tri right before exams. 

Dillon's Conclusion  

Overall in this Dev project I learned how to do and understand the inverse graphing a bit more and how the X and Y axis basically swap.  With the normal graphing of  COS I already pretty much had that down but was nice to just review over the problem once more.  Shaun helped me a bit on the inverse problem and also explaining how to do a lot of the problems from the homework and how to do them.  This all helps me very much to prepare myself on the upcoming exam we are going to be doing very soon.  The devs are a nice thing to kind of look at what other people did as well and see how they might see problems.  It is very interesting looking at what other people have posted onto the blogger.  Lastly because of the Dev projects I am feeling more confident than I was before coming up to this exam.

DEV!

Find solutions for 0<Ø<2π

You are going to solve this as you would an algebraic equation. First, add 20 to each side then divide by two. This leaves you with cosecant of theta equals 2. Cosecant is the reciprocal of sine, so cosecant of theta equals 2 becomes sine of theta equals1/2. On the unit circle, sine is the "y" coordinate, so you want to look for where "y" is a positive 1/2. This happens at π/6 and 5π/6. 

This is also going to be solved algebraically. First, add 3 to both sides, then divide by 4/3. This ends up becoming cosine of 2 theta equals 1/2. The two solutions are π/3 and 5π/3. Because it is cosine of 2 theta, the period is only pi instead if 2π. Set 2 theta equal to equal radian solution and solve for theta. The two new solutions are π/6 and 5π/6. Because you are solving for all solutions less than 2π, you need to ass a period to each solution. This is shown above. Your final four solutions are π/6, 5π/6, 7π/6, 11π/6. 

Graph the equation 

The first step to graphing is to determine the equation's amplitude, period, phase shift, and vertical shift. Always start graphing with five "nice" theta points. These will be the "x" values of the graph. These are 0, π/2, π, 3π/2, 2π. You will apply any transformations to these values. The phase shift is subtracting π/3 from each value because it shifted to the left by a value of π/3. The work for this is shown above. The "y" values for a sine graph are 0, 1, 0, -1, 0. Just like with the theta values, any transformations will be applied to these values. 

This is what the graph will look like after being graphed. You can see the phase shift to the left and the vertical shift down. 

Solving for inverse functions 

Sine is opposite over hypotenuse, so 12 is one leg and 13 is the hypotenuse. Then, use Pythagorean theorem to solve for the other leg, which 5. Tangent is opposite leg over adjacent leg, so the solution is 12/5. 

This problem begins the same as the one above. Because it is inverse of 2 tangent, you use the double angle formula. Plug in the sine and cosine values from the triangle and multiply across. The solution is 24/25. 

How many radians do the minute and hour hand move from noon to 5:30? 

Since there are 12 chunks on the clock, each one is 1/12 of the circle. To find the radian measure, multiply 1/12 by 2π. Each chunk is π/6. The hands move 5π/6 radians when it's 5:00. 5:30 is halfway between 5 and 6. To find that radian measure, multiply 1/2 by π/6 to get π/12. To find the total amount of radians the hands travel, add 5π/6 and π/12 to get 11π/12. This means the minute and hour hands travel 11π/12 radians from noon to 5:30. 

Reflection: 

I chose to do two solving problems because solving was something I really enjoyed during this class. I really enjoy algebra and this was similar to solving in algebra. It was kind of like a puzzle finding the theta value you just solved for. 

I did a graphing problem because that was an area I struggled with. Doing that problem and explaining it really helped me understand how to graph more. I needed to know how to do the problem, and how to explain it, which is something I wasn't able to do before. 

I did two inverse problems because I also enjoyed doing those. It brought back some triangle trigonometry, which was something I enjoyed from geometry. I also liked how you could use, for example, sine inverse to find tangent. 

My last problem was a clock problem. I really struggled with these when we first learned them. After going away from them and coming back, I'm able to understand them easier. I really like how you have to find out what fraction of an hour the minute hand has traveled to find the radian measure. 

For my problems, I chose two that I really enjoyed doing and two that I really struggled with. Making up problems for something I had struggled with was a huge challenge for me, but it really helped me to understand the type of problem a lot more. Doing two problems that I understood and enjoyed was more fun for me because I could work backwards to figure out a problem. 

D.E.V. project

https://www.dropbox.com/s/rtyrtieavsc7s0l/math%20project%202.pptx
This project was very stressful for me. I think it was stressful because I really didn't know what I was doing. I really had trouble this trimester with the things we were learning about more than functions. Functions I was able to take what I learned and create problems that were difficult for me to solve. This trimester I didn't even know where to begin. I would sometimes sit in my room for hours just trying to think of the perfect problem to construct. I would think of an problem and then realize I couldn't solve it myself how was I supposed to expect myself to explain to other people? I tried to look at example problems we had done but they weren't that much harder. While most of these problems I constructed aren't hard I hope you understand that some of the simplest problems were the ones that were the hardest for me. I really did try to tackle the problems that I had the hardest time with.

Thu

D.E.V. Project

Here is my D.E.V. Project. My reflection is included in the powerpoint. 

~Stephany

DEV PROJECT

More PowerPoint presentations from Stephany Marie

D.E.V project

By Alexis, http://247594159603412126.weebly.com/index.html
My reflection is also on there! Thank you Mr. Jackson.

Vance's D.E.V. Project

Here is my D.E.V.

My reflection is in the prezi itself.


I recommend going into full-screen mode as a graph that is in the presentation gets messed up at this size.

Hannah, Hilary, Amber DEV

DEV from Amber Dockter

D.E.V. - Nianqing

DEV project :)

https://docs.google.com/file/d/0BzeL6czieasOWl9FNXFyNmVyT3M/edit?usp=sharing

Annette and Kevin's DEV project

DEV Project

Problem #1:

 

Solve the equation for 0 £ q < 2p

The equation is:

4+cos q = (8 + Ö2) / 2

Step 1: Subtract 4 from both sides. One side you will subtract 8/2.

4+cos q = (8 + Ö2) / 2

-4                      -8/2

Step 2: Because there are common denominators the two fractions can be subtracted. For example,

8-8 = 0, so you would end up with Ö2/2.

Cos q = Ö2/2

Step 3: Use the unit circle to find q. Look for the angles with a cosine of Ö2/2. 

q = p/4, 7p/4

 

Problem #2:

 

Find the period, amplitude, vertical shift, and phase shift of this equation and graph it.

y = 2cos (q - (3p/4)) + 6

Step 1:  The typical formula for graphing sine and cosine functions is a ´ cosb (x-h) + k. "h" represents the horizontal, or phase, shift. "k" represents the vertical shift. "a" is the amplitude and "b" is the horizontal stretch.

First we need to find the period of the graph. The new period can be found using 2p/b. "b" = 1 in this case so the period would be 2p

 

Step 2: Amplitude needs to be found next. The amplitude is 2 in this case.

y = 2cos (q - (3p/4)) + 6

Step 3: The next part of the equation we must find is the vertical shift represented by the variable "k." The vertical shift in this equation is 6.

y = 2cos (q - (3p/4)) + 6

 

Step 4: The last item we need to find is the phase shift. When the phase shift is subtracted in the equation it is positive on the graph. When it is added in the equation it is negative on the graph.

y = 2cos (q - (3p/4)) + 6

 

The phase shift in this equation is positive3p/4.

Step 5: Now we need to graph this equation.

First list the angles used for Cosine.

Cosq: 0, p/2, p, 3p/2, 2p

Then add 3p/4  to each angle.

3p/4 + Cosq: 3p/4, 5p/4, 7p/4, 9p/4, 11p/4

Second, list the y-values. 

y: 1, 0, -1, 0, 1

Then multiply the y-values by 2 and add 6.

6 + 2y: 8, 6, 4, 6, 8

 

Now graph the whole equation. (I was not able to get a picture of the graph onto the blog post)

Problem #3:

Simplify the trigonometric expression,

(tanq ´ cosq)/(cotq ´ sinq)

First, rewrite the equation in terms of sin or cos.

((sin q/ cos q) ´ (cos q/ 1))/((cos q/ sin q) ´ (sin q/1))

Now look to see if any of the variables cancel out.

((sin q/ cos q) ´ (cos q/ 1))/((cos q/ sin q) ´ (sin q/1))

The two cosines in the numerator cancel out, and so do the two sines in the denominator.

This leaves us with

sinq / cosq = tanq

 

Problem #4

Solve the equation for 0 £ q < 360.

-2 + tan q = (-6 + Ö3)/3

First add 2 to each side. (on one side it will be added like 6/3)

-2 + tan q = (-6 + Ö3)/3

+2                           +6/3

This leaves you with:

tan q = Ö3/3

Now we need to find what q equals. To find the tangent of something you need to divide its sine by its cosine. These are the three options we have.

(Ö2/2)/(Ö2/2) = 1

(Ö3/2)/(1/2) = Ö3/3

(1/2)/(Ö3/2) = Ö3

The only one that equals Ö3/3 is (Ö3/2)/(1/2). Now find which angles have a sine of Ö3/2 and a cosine of 1/2 and whose tangents equal a positive Ö3/3.

q = 30°, 210°

 

 

 

 

 

 

 

 

 

 

 

Reflection:

I tried to choose one problem for each of the units we have worked on this trimester. I chose to do it this way so I could use the project as a form of review for the final exam. These problems are an example of the parts of each unit that a understood the best and knew really well. I did not learn anything new with this assignment, but I did see it as a very fun way to review and challenge myself on a level I never really have before.