Student Problem Unit R Concept 3

This is a type 2 problem from Unit R concept 3. There is ambiguity in the problem but using the first quadrant is always the most ideal choice. This type of problem requires knowledge on the unit circle as there are angles and radicals that are to be dealt with. This problem will show the reader how to solve a type of type 2 problem.

The reader must pay attention to the steps and understand how the formula got on there. The reader must understand the use of quadrant 1 as first priority and then they must learn to plug them together to get the final product.

Student Problem: Unit R Concept 2

This is about how to use the sum and difference formulas when given values for right triangles. First, you have to draw the triangles in the correct quadrants. Next you have to find the missing piece of the triangle. Now, the numbers need to plug into the sum and difference formulas. In this case, the formulas sin(u+v) and tan(u-v).

The readers need to pay attention to the quadrants of the triangles. They also need to pay attention to what is positive and negative. The hypotheses will be positive. There are two triangles that lie in two different quadrants, II and I.Quadrant II. To solve for tangent, the readers can multiply by common denominator and solve for it. 

Student Problem 1 Unit R

Sum Formulas 

Difference Formula

1. These pictures show two ways of finding the exact values of the sine, cosine, and tangent of 165 degrees. This is Unit R Concept 1 which is about finding the exact values of angles that aren't on the Unit Circle. We use the angles on the unit circle that can add or subtract to that angle. The answers of the trigonometry functions of that angle must be the same. Using the Sum and Difference Formulas, we can plug in the numbers to find the answers. 
2. What does the reader need to pay attention to?
The readers need to be careful when they are trying to solve when there is a negative. The solution is knowing which part is negative, and which part is not. When solving for tangent the reader needs to pay a very close step in solving for tangent because we don't solve it all the way through, we have to multiply by its opposite, then foil and solve.

Unit Q 3 Concept 4 problems

Level 1                  cosx=1

Level 2                                   2sinx-1=0

Level 3                     2sin^2x-3sinx+1=0

Level 4                              csc4x=2

Unit Q 2 Solve with identities and right triangle

How to solve using identities:

How to solve using identities:

How to solve using SOH CAH TOA

How to solve using the unit circle

Unit Q 1 Pythagorean Identities Derivation

The formula above comes from the Pythagorean Theorem (y^2+x^2=r^2).  The triangle would look like the picture on the right, which is labeled y, x, and r.  So, if we look at the triangle, we can see that sin^2 in the Pythagorean Identity is y because sin is opp/hyp.  Cos^2 is x on the right triangle because cos is adj/hyp, and 1 is r because r will always equal 1 in this case of the unit circle.

To get the second main (tan^2x+1=sec^2x) identity we do the following below:



















Now to get the 1+cot^2x=csc^2x identity we do the following below:

Math Analysis Reflective Blog Post

1. How have you performed on the Unit O and P tests?  What evidence do you have from your work in the unit that supports your test grade (good or bad)?  Be specific and include a minimum of three pieces of evidence.

I have preformed poorly on both tests, I have shown low quiz scores on certain concepts that I found were difficult. I've shown not to practice well in the quizzes or I just finish the quizzes for the sake of finishing.

2. You are able to learn material in a variety of ways in Math Analysis.  It generally follows this pattern:

→ Your initial source of information is generally the video lessons and SSS packets followed by a processing and reflection activity via the WSQ
→ individual supplemental research online or in the textbook before class
→ reviewing and accessing supplementary resources provided by Mrs. Kirch on the blog
→  discussion with classmates about key concepts
→ practice of math concepts through PQs
→ formatively assessing your progress through concept quizzes
→ cumulatively reviewing material through PTs
→ Final Assessment via Unit Test.

Talk through each of the steps given in the following terms:
a. How seriously do you take this step for your learning?  What evidence do you have to support your claim?  Make sure to make reference to all 8 steps.
b. How could you improve your focus and attention on this step to improve your mastery of the material?  What specific next steps would this entail?  Make sure to make reference to all 8 steps.

• I don't always put a lot of effort on my WSQ's because I want usually want to finish them as soon as possible. I always highlight important information and write down the key pop-ups that you include during the video. I tend to finish what I need to do in order to complete the WSQ. The times when we have to complete extra practice problems, I don't watch the entire video. I skip to the answer to check if I have the answers right, but that is as far as I go. It is helpful to see how the problem is done and hear why certain steps must be done in that way. Looking at the big picture, I will develop the skills to explain the steps to solving for the problem and move me further to understanding the concept.
• Your SSS packets along with the videos for each concept provide us with more detailed information than the textbook. If I need further practice, I use the extra practice problems from the blog for the countless problems they have. I could improve my attention to this step by completing more practice problems from the blog if I want to practice for the test. This would add to my mastery of the material by doing additional work to the extra practice I normally do.
• I don't always look at the supplementary resources. I am consumed with other homework and struggling to finish so that I can sleep. I do however look at them when I do have the time or when I need to study for the test. I will try to pay more attention to these if I can.
• I have found this to be important to my understanding of concepts. We help each other out when we don't understand how to do the concept. When we discuss, we find that the person who is verbally explaining how the concept works applies it in a way that makes sense. If there was a way to improve the group I'd say we should improve our communication skills when it comes to math material. If all of us are clueless, or if only one of the 3 grasp what is going on, we ask Mrs. Kirch for further explanation and then we try to explain what she said to ourselves in terms of our own words and this always seems to help us.
• PQ's are so useful and helpful and they are the practice that I need. If I practice the PQ's I can get a good grip on the concept. PQ's are what I need to master the concept. I don't focus much on this even though I need to. I really need to do all my PQs to practice and improve myself.
• The quizzes showed if I understood how to do the concept. I could improve my attention on this step by re-taking the some of the few quizzes that I didn't get an 8 on.
• I don't think I took the PT's seriously, Most;y I just tried finishing PT's for the sak of finishing, for almost every WSQ I would finish everything but the last part of the PT's and it would get me stuck. I was able to understand where I lacked and where I good at with PT's though. Improvement wise, I think by taking the PT's more seriously, I can get a feel of the test and gt a higher score on the test.
• The final assessment is what sometimes shows how well I put effort into trying to learn the Unit. When I get my quiz scores or when I do my PT's and PQ's reflects on the tests. There are times when I work hard and then don't get the score I want because I did dumb mistakes or something. When I overlook at the tests I begin to show mastery when I start studying to retake the test, seeing my mistakes and trying to fix them helps a lot. What I could improve though is that I need to answer the questions carefully and show every small part that will get my answer correct.

3. Reflect on your learning this year thus far by considering the following questions:
a.  How confident do you generally feel on the day of a Unit Test?  Give evidence and specifics to back up your answer.
b.  How well do you feel you have learned the math material this year as compared to your previous years in math? Give evidence to support your claim.
c.  How DEEPLY do you feel you have learned the math material this year as compared to your previous years in math?  Give evidence to support your claim.
d.  Do you normally feel like you understand the WHY behind the math and not just the WHAT/HOW?  Meaning, do you understand why things work, how they are connected to each other, etc, and not just the procedures?  Explain your answer in detail and cite specific evidence from this year.
e. How does your work ethic relate to your performance and success?  What is the value of work ethic in real life?

• I normally feel scared on the day of the Unit Test. I'll get scared if there were pieces of things that I was suppose to turn in but I didn't and then trying to quickly finish the test. I normally study for the test, too by reviewing everything in the Unit.
• This is one of the first few times where I actually learned something in math and remembered it well. Compared with my other math teachers, there are times where I just learn something and I forget it the other day, but with this class I was able to understand it better.
• I believe that, out of all my years in Segerstrom, this has been the year that I have understood math the most. In all my other years of math, I understood the concepts, but it was only to an extent. I mean I understood it, but I wouldn't be able to explain it that well. This year, I can confidently explain the concepts to anyone who's having trouble.
• I do understand the "why" behind the math concepts, not just the "what/how." I understand the "why" because during the school year, many of my group mates would ask "why" in regards to the concepts and I would be able to give them the answer if I knew it. I was able to learn this through the videos that you made for us which explains why this is so.
• My work ethic is terrible. Normally I would do the homework and practice but then for some parts it was for the sake of finishing. Sometimes my work ethic does show my performance on a test, but other times it doesn't. I remember getting almost all 8's on my quizzes but then getting a C on Unit M, I even knew how to explain how to do it and why it is that, I helped people who needed the help and ironically they get higher scores than I did. Then there's Unit N where I did crappy on the practice and the quizzes, but great on the test. But I'd say my effort on the practice affects me a lot on the test. The value of work ethic is important in life because a lousy work ethic can affect everything I do in life.

WPP 13-14