Student Problem #3

What is this problem about?
This problem is about using the sum and difference formula to prove the trig of an inverse trig function.

What does the reader have to pay attention to in order to not make a mistake?
The reader must pay attention to how the the trig expression was converted to an algebraic expression. Pay close attention to how the Unit Circle values was substituted into the problem. Make sure to always use the first quadrant when you're left with ambiguity (ex: sin (0) could equal = (1, 0) or (-1, 0) but we use (1, 0) in this problem because it's part of the first quadrant.) Remember that cos = x, sin = y, and tan equals y/x :)

Student Problem #2

Given: cosu = -5/13 (3rd quadrant) & sinv = 15/17 (1st quadrant). Find sin(u+v) and tan(u-v).

 *on the left side I meant to put "left and down = negative" not left and right.. 

What is this problem about?
This problem is about using the sum and difference formulas when given values for right triangles. You are given two values of sin/cos/tan and plugging it into the sum and difference formulas.

What must the reader pay close attention to in order to not make a mistake?
The reader must pay close attention to drawing their triangle correctly. They must make sure it fits the quadrant. They also must make sure the signs are all correct and fits ASTC depending on which quadrant it is. They also must make sure to utilize the sum/difference formulas correctly (simplifying/multiplying fractions)..

Student Problem #1: Unit R Concept 1

285 degrees.

Difference formula

Sum formula

What is this problem about?
This problem is about finding the exact value of sums and differences using the sum and difference formulas.  We find the exact values for sine, cosine, and tangent of the angle by figuring out what angles to use by adding/subtracting to the angle we want. 

What must the reader pay close attention to in order not to make a mistake? 
The reader must pay close attention to how the sum and difference formulas are used. They should also pay cloe attention to how we are able to find the angle we want by using addition/subtraction with the degrees of the unit circle. Remember that there are many options to finding the angle we want and they all lead to the same answer.

Blog Post #3

Unit Q Blog Post #2

Blog Post #1

Show and explain how to derive the two remaining Pythagorean Identities from sin2x+cos2x=1. Make sure to include in the beginning where sin2x+cos2x=1 comes from to begin with (think Unit Circle!)

Pythagorean theorem : x^2 +y^2 = r^2

Sin^2x +cos^2x = 1. We know that sin = y/r & cos = x/r. Therefore, we can substitute that in -> (y/r)^2 + (x/r)^2 = 1. We also know that r = 1. If we substitute '1' for 'r' into the equation we would get -> y^2 + x^2 = 1, and since 1 = r, the equation becomes: y^2 + x^2 = r^2.

1 + tan^2x = sec^2x. Using cos^2 + sin^2 = 1, we will be able to decipher where 1 + tan^2x = sec^2x comes from. First, we divide cos^2 + sin^2 = 1 by cos^2 (x/r). 

(x/r) + (y/r) = 1 divided by (x/r). We can cancel out cos^2 (x/r) and end up with 1. Dividing (y/r) by (x/r) will give us (y/x), also known as tan^2. And dividing 1 by cos^2 will give us (r/x), also known as sec^2 - > 1 + tan^2 = sec^2.

1 + cot^2 = csc^2. Using cos^2 + sin^2 = 1, we will be able to decipher where 1 + cot^2 = csc^2 comes from. First we divide cos^2 + sin^2 = 1 by sin^2 (y/r). Dividing cos^2 (x/r) by sin^2 (y/r) will give us (x/y) which will give us cot^2. Dividing sin^2 (y/r) by  sin^2  (y/r) will give us 1. Dividing 1 by sin^2 (y/r) will give us r/y.. which is csc^2 -> 1 + cot^2 = csc^2.

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.

RESPOND HERE: I performed terribly on the Unit O test the first time I took the test. I scored a 64%, I believe. It was because I barely reviewed the SSS packets mainly because I was overly confident that I knew the material from the scores of 8's of my Unit O quizzes. NEVER AGAIN! - I never want to take so much time out of my day to go to the tutoring sessions and do all of that extra work again. The second time I took the Unit O I did better because I reviewed - 91%. I performed okay on the first time I took the Unit P test - 88%. It was concept 6 (using law of sines with word problems) that really screwed me up.. My quiz scores were mainly 7's and 8's. I should have studied the SSS problems more closely and reviewed more.

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.

RESPOND HERE: I really do pay attention to the video lessons. In the beginning of the year, I used to not take them as seriously because I never really acknowledged how beneficial they were and how much I would struggle without watching them. I always stay focused when watching the videos and I re-watch them till I completely understand and can answer the WSQs without hesitation. I've never used the textbook or any additional supplementary resources provided by Mrs. Kirch because I never really needed to. I believe the SSS packets already helps enough. I only take the discussion with classmates about key concepts seriously if the concept is difficult for me to understand. If I need help on something, usually staying focusing during the discussions are helpful. I take the PQs pretty seriously because they help me show if I can understand how to solve each problem and understand the concept. I don't think I need to improve my focus/attention on PQs when I'm already putting enough effort into them. The concept quizzes help a lot because they show me if I understand the concept without any resources so I take them seriously as well. I guess one thing I could improve my focus and attention into the concept quizzes would be to not study the concept last minute right before the quiz because I usually forgot the material later, so I should continuously review the concept. PTs are definitely important. I always complete the PTs because they help show me if I remember the material and they also show me if I remember concepts from previous units. I can improve my focus/attention on PTs through reviewing my work for each concept before the test. The Unit Test helps display my complete understanding of ALL the concepts from the Unit. I always review the SSS packets and quizzes before the unit test to make sure I've mastered the concept.


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?

RESPOND HERE: I usually feel pretty confident the day before the Unit Test. This is mainly because of all the pqs and pts that Kirch assigns to make sure I've mastered the concepts. I guess compared to my previous years in math, this year has given me the most help. With all the extra work and resources from the SSS packets, they make sure I COMPLETELY understand the material. I definitely do feel I have learned the math material because I finally understand the background of the math concepts. The math material made more sense as I was able to learn more about the derivation of the angles/triangles and how they relate the Unit Circle, and also the different types of laws (cosines/sines) and formulas.The derivation of the concepts help me understand how the concepts are connected together. At the beginning of the year.. I felt unfortunate to be forced to do all of this work and felt there was no reason behind the "flipped classroom." Now, with all the times Kirch has emphasized the real significance of the all the assigned work and how it is supposed to benefit ourselves - I felt more motivated. With this class, I've seen that all the times I've become careless, the results show. I've learned that it's more difficult to catch up with the material when you aren't on pace with the rest of the class. It's stressful and definitely not worth it :( The same goes with real life. With a strong work ethic, you will be able to become more productive and more capable of succeeding in a work environment.

WPP #14: Unit P Concept 7

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WPP #13: Unit P Concept 6

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