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.

Sophie and Haley's D.E.V. Project

These are our videos: 














Reflections:


The reason why we chose the concepts we did was because we understood them the most. We did a graphing problem, a wheel problem, two verifying problems, and a problem where you had to find the exact values of three different values. Haley and I understood these types of problems the best, and whenever your trying to teach someone something, its best to understand the material to your fullest ability. These problems provide an overview of our best mathematical understanding thus far, because we chose a variety of problems from different units. Our first problem, which was a graphing problem, was from unit two, the graphing unit. Our second problem was a wheel problem from unit two. Our third and fifth problems were verifying problems from unit three, the identities unit. Lastly our fourth problem was from the first unit of measurement, and we did a problem where you had to find the exact values of three problems. Overall this project was a good review of what we’ve learned thus far. Therefore, I was reviewing and relearning problems and concepts that I’ve learned so far in the class. For this reason I feel like this project was educationally valuable, and made us dig deeper and expand on concepts that we’ve learned thus far in the class. -Sophie 




The reason why we chose to create our problems was because we wanted them to be on the more challenging side. We wanted something that was not too easy but challenging so that we would understand how to solve them. These problems cover all of the units that we learned. So, they provide an overview of the best mathematical understanding of what we learned this trimester in class. We wanted to make our project diverse, so we managed to cover some of the main material in each unit. This shows that we learned a lot over the units. I learned a lot from this assignment. I did not know how difficult it would be to actually come up with problems on our own. I thought that it would be really easy, however, it was actually quite a challenge. It was difficult coming up with hard problems because you actually have to solve for them. This project helped me understand how the units are all related. It also really helps you study for the exam because you are looking over all your materials. Overall, this project was very helpful and enjoyable. -Haley

Bob

The identities unit was a struggle just like all of the others. It was probably the easiest of the three units though. My fuzziest point in this unit was solving equations with tangent in it. First you had to know that tan=sin/cos. and then you had to get common dinominators and then flip and multiply. This whole process really confused me and I would always mess up one step in the process and that would give me a wrong answer. Although this was my fuzziest point in the unit I feel like I finally got it down by the time the test came around and I feel like I did well on the test.

B.O.B

During the couple of weeks that we worked on the past unit I found this unit was easier than the last two units.  I did not seem to have much problems doing the work and if I did I went in and got help from Mr. Jackson or help from my dad.  This unit was shorter than the other units in precalc trig.  Although I may not have gotten some questions right I still believe that I did exceptional in class.  My muddiest point was when I got confused how to complete and break down some of the problems. When I finally understood that you could use the equations to help you I started understanding more and making sure I got the problems right by checking with Mr. Jacksons problems.  Whenever I double check problema I make sure that I didn't mess up anywhere and get the whole problem right or else I won't understand how I did it for later references.  P.s. I'm sorry this blog is late. Thank you for letting me post still.

This unit was pretty easy for me. the only problem I really had with it was knowing when to use the double angle/half angle identities and I also kept thinking that sin(x +cos(x equaled 1 when it was only sin^2(x +cos^2(x that equaled 1.

Your plan has just been foiled

Identities (bob#4?)

Ok, my muddiest point this unit would honestly have to be the mud I put myself into. I have a range of challenging or pushing courses this trimester and the workload has been difficult with my schedule. Not prioritizing correctly or studying for this class as much as I probably should has affected me. I'm a straight A student with a B in this class, hmm. ;) If I could dispense any wisdom; stay on top of things and don't let yourself think you know the material if you sort-of don't. The identities unit took some stuff out of me, but I'm made up my loses and I'm hoping to pull through :)

Annie

The muddiest point for me this unit was the converting of the different sin and cos and tan unit conversions. Especially the usin of all the different formulas really made me struggle. However i was able to push past those formulas and towards the end of the unit, I had a full grasp of the information provided in the unit.

B.O.B. - Identities

For the first time this trimester, I actually found the coursework to be challenging and had to really think about what I was doing to figure out the answers. A bit cocky? Maybe, but at least I can admit my weaknesses, and this unit was full of them. I was so thankful that Jackson moved the test back, because after I missed Monday the 13th, I fell into a "Wait, what am I supposed to do?" slump and my, oh, my if that wasn't hard to crawl out of. But, with classmates being classmates and Jackson being Jackson, I slowly climbed out of there and figured out how to prove those pesky identities. This unit was by far the most challenging and interesting and I'm glad people around me were able to help me figure it all out.

Muddiest Point

My muddiest point in the identities unit would have to be verifying. I knew the concept of verifying, however I had a hard time with getting both equations to equal each other. If you mad one small mistake then the whole problem would be different. I had to be extremely careful with what I was doing and I often found myself double-checking what I did. Near the end of the unit I found that I was starting to do well with them because of all the practice I had.

BOB reflective

I feel like this was the easiest unit so far for me to understand, I feel as if I see the identities right away and then completing the problem was a snap. Really the only problems I have had this unit are when I don't look at my formula page and don't think oh yeah this is the same as doing this, either way this time around was a lot easier than the last couple of units.

B.O.B

The hardest part if this unit was verifying the problems. I could get one side usually finished but I seemed to have problems getting the other one to equal each other.  One would be easy and the other would be more difficult but it kinda hot easier as time goes on but it's still kind of hard to figure out. 

B.O.B.

In physics we are learing the Law of Sines. Soon as Shoe started teaching us about it i thought of Pre Calc class and how we have been working with  Sine, Cosine, and tangent ect. I have realized that this partiular topic or section in math is used throughout your high school career!

b.o.b muddiest point- identities

My muddiest point for this unit was verifying identities. Simplifying was very easy and finding the exact value in radians was fairly simple, but the verifying I found difficult. Mainly the ones having to do with tangent though. Those really through me off, I don't know when my exact moment of clarity with that was, maybe when I was doing the review but I still found that the hardest part throughout this unit.

B.O.B. Muddiest Point

My muddiest point for this unit was when we started working with secant, cosecant and cotangent. I was a little slower at totally getting the identities with sine, cosine and tangent and so when we moved on, I was not quite ready. The more practice I did, the better I became. The identities were more obvious and I could pick them out and solve, simplify or verify much quicker. The end of the year is fast approaching so that is adding some pressure, especially in this class to not fall behind at all. If anyone else is stressed out, remember help is avaliable!!

B.O.B.

This unit was quite difficult to begin with. We were barraged with many equations and tactics on what to do. I enjoy the things learned in this unit we just learned them at a faster pace than usual (which isn't always bad). I enjoyed the trig identities and simplifying portion the most, it came easier and had good application. I'm nervous about the test I had a few complications such as problem 4. The tri. went by fast and I feel I learned quite a bit, and I've enjoyed the class so far, although I'm slightly iffy about the D.E.V. 

B.O.B identities

Reflecting back on this unit I would have to say I somewhat liked it.  Though at first it was hard because I missed a few days so I was behind, but with the homework I started to get better at solving identies.  Also for me it was tough to identify what identity I should use to start a problem where you had to prove an identity.   After I got over that bump it was easy to solve using algebra skills.  I enjoyed the algebra because for me it is easier to do than the previous units.  Finally this unit had it's ups and downs but in the end I enjoyed it.

B.O.B.-Muddiest Point

The Trigonometric Identities Unit was a very tough unit for me! This was probably one of the hardest units in all of my math classes throughout school. Recognizing the identities and substituting was not hard at all but solving and where to go once you get stuck were both huge problems for me. The first problems we did with simplifying trigonometric identities went well and was a breeze once I understood how to recognize the identities and to substitute them in. Once the problems became harder and more complicated, I came to a screeching halt. I was confused on what to do to get started but usually after I was heading in the right direction I could figure out where to go from there. But when I got stuck, I was stuck! I looked at the answer key to find out where to go or I got help from Mr. Jackson or a classmate around me. The double angles, sum/difference identities, product to sums identities, and the half angle identities were all the easiest part of this unit for me. I understood what to do and I felt the algebra was fairly easy. I felt confident about those parts of the test but I'm not so sure about the verifying part of the test.

BOB

At the beginning of the unit when we got the formula sheet, I was very overwhelmed. The formulas looked very confusing when we first started using them. The ones that really confused me were when  we had to use a formula but then simplify it to prove that it matches the other side. When we simplified, I tended to get lost in all of the radicals and fractions, which I know is totally my fault for not being better at simplifying.  Towards the end, once I did a lot more of them, I felt a lot more comfortable with this unit and actually began to like it.

Erin :)

bob

Starting this unit when Mr. Jackson said it was going to be mostly algebra I was excited about that because algebra has been my favorite math subject. Then he handed us a bunch of sheets with different formulas on it and I only half payed attention to it and tried to start working. It was really challenging because I couldn't always remember that cosine squared of theta plus sine squared of theta equals one. Then I had to tell myself stop being silly and use your formula's and it made everything much easier. 

BOB

This unit certainly had its ups and downs.  My mind was never able to get into the mindset of picking out the identities from equations.  Many of the problems that could be solved easily using an identity, I simply overlooked, created a much more difficult challenge for myself.  Also in many cases I would make a small mistake somewhere along the line and struggle to find where that mistake was made in order to complete the problem. All in all I felt like this was not the most difficult unit, but definitely challenging.  It really tested my ability and made me learn to take a longer look at each problem before just jumping right in.  If I jump in too quick, I make mistakes and am forced to try the problem again.
-Doug

Moment of clarity

I was hoping that since this unit was completely new I wouldn't have a hard time learning it. However, I was completely wrong. I really struggled with this unit and for the first couple of days I really had no idea what I was doing.Everything was just a jumble of numbers and words to me.  The stuff that really threw me off were the simplifying of functions and verifying them. I think what made it hard was the fact that I was just getting use to these identities. Sometimes I would take the long route to solve a problem and then realize that I could have used an identity to solve it and it would have been much faster. I don't know how or why I eventually was able to solve these problems, but I guess it was just practicing. Yesterday as I was doing the review the answers came to me so easily. I think it really helped that I became familiar with the identities so I could tell when this= this or these to make a one. I guess practice is really what helped me get better at simplifying.

Thu

B.O.B for Trig Identities

This unit seemed to make a lot of sense.  The biggest part was figuring out how to manipulate each side of the equation to get to your desired expression.  It felt like a puzzle in that the goal was to move the pieces/identities around until both sides of the equation were equal.  The half angle and double angle formulas were not that bad consideirng we had a formula page.  It was similar to physics because you had to identify what you had and which equation made sense to use.  If you could make sense of the formula page and pick out what you needed, the ideas were pretty straight-forward.  The idea of verifying equations made sense to me especially as I tried ot keep the sin cos and tan functions as variables.  I also tried to keep the equation clean by getting rid of the theta or x at the beginning and then plugging it back until the end.  Obviously this cannot happen with the half/double angle formulas but it seemed to help with everything else.