Well this could be my very last comment post on this blog. Its been a nice and valuable experience to mentor such a good group of people. Its been a nice run and hopefully i can still do it for next year, even though I'm going to be busy with my university studies. I might have to email Mr. K next year if i can mentor his Precalculus and AP calculus classes next year. I think i should stop now because the thought of having my last class with Mr. K really makes me sad, so without further ado here is my comment on Francis's post:

Francis,

That was an amazing poem you made, you deserve some major props for that. Today was not really the last class , tomorrow will be the last class. I kinda feel sad because it is going to be my last class with Mr. K, while you guys still have the chance to become his student next year IF you take AP Calculus. I will definitely miss his skits that make the class very interesting.

-m@rk

## Thursday, June 5, 2008

## Sunday, June 1, 2008

### Probability

There is only about 5 school days before the provincial exams and it seems like the class is a little trouble in time.

Nelsa,

Great scribe post! I am really impress on how thoroughly explained your scribe post is. I really struggled in probability ever since grade 9 and is one of the reasons why i took this class again. Its too bad to hear that we are not going to have a test for this unit, because i really want to measure my expertise in this. BTW, good luck on your provincial exam tomorrow.

-m@rk

Nelsa,

Great scribe post! I am really impress on how thoroughly explained your scribe post is. I really struggled in probability ever since grade 9 and is one of the reasons why i took this class again. Its too bad to hear that we are not going to have a test for this unit, because i really want to measure my expertise in this. BTW, good luck on your provincial exam tomorrow.

-m@rk

## Monday, May 19, 2008

### Conics quizzes

Well, since i heard that the test for this unit is coming very soon I decided to compile a bunch of links that will help all of us to study, so without further ado here it is:

Link 1

Link 2

Link 3

Link 4

Link 5

Link 6

Link 7

Link 8

I hope that those links will be very useful to all of us on the upcoming test and especially the provincial exams which is only 20 days away. Leave a feedback if any of those links doesn't work.

-m@rk

Link 1

Link 2

Link 3

Link 4

Link 5

Link 6

Link 7

Link 8

I hope that those links will be very useful to all of us on the upcoming test and especially the provincial exams which is only 20 days away. Leave a feedback if any of those links doesn't work.

-m@rk

### Difference between a hyperbola and ellipse

This was a comment that I made regarding Joyce's BOB post.

Joyce,

After reading your BOB post, I can see that you are having troubles with the differences between the standard form of ellipse and hyperbola. They are very similar and sometimes hard to distinguish because Mr. K might algebraically massage them and make them look harder than they actually are. I think that there is only one difference between them. On a ellipse the terms are suppose to have the same signs. On the other hand, on the hyperbola the terms should have opposite signs. To further enhance your learning about this you can check this out: http://people.richland.edu/james/lecture/m116/conics/conics.html

Joyce,

After reading your BOB post, I can see that you are having troubles with the differences between the standard form of ellipse and hyperbola. They are very similar and sometimes hard to distinguish because Mr. K might algebraically massage them and make them look harder than they actually are. I think that there is only one difference between them. On a ellipse the terms are suppose to have the same signs. On the other hand, on the hyperbola the terms should have opposite signs. To further enhance your learning about this you can check this out: http://people.richland.edu/james/lecture/m116/conics/conics.html

## Thursday, May 15, 2008

### Hyperbolas

Since my AP exam is done I can now go back to my mentoring duties and probably swing by my precalculus class once in a while. This is my comment on Francis's scribe post concerning hyperbolas. Anyways this is only my 22nd post so i got to increase the frequency of my post and the quality of my work.

Francis,

I know that this comment is about a day late but they always say that its better late than never. I really like how you illustrate the step by step process of how you get the answer. It kinda shows the missing pieces of information that are not on the slides. It helps someone like me who doesn't remember a single thing from the conics section to recall everything. Thank you and job well done. Since my AP class is over , shall i say that I'll see you in class tomorrow.

-m@rk

Francis,

I know that this comment is about a day late but they always say that its better late than never. I really like how you illustrate the step by step process of how you get the answer. It kinda shows the missing pieces of information that are not on the slides. It helps someone like me who doesn't remember a single thing from the conics section to recall everything. Thank you and job well done. Since my AP class is over , shall i say that I'll see you in class tomorrow.

-m@rk

## Saturday, May 3, 2008

### The secret of Pascal's Triangle

Benofschool,

Very well summarized scribe post. It really helped me refresh my memory.Anyways, for your challenge on finding the fibonacci sequence on the triangle. The fibonacci sequence can be found by getting the sum of the numbers diagonally. This is very well explained here: http://goldennumber.net/pascal.htm.

Lastly, a little spoiler for your next class is also on that site.

-m@rk

Very well summarized scribe post. It really helped me refresh my memory.Anyways, for your challenge on finding the fibonacci sequence on the triangle. The fibonacci sequence can be found by getting the sum of the numbers diagonally. This is very well explained here: http://goldennumber.net/pascal.htm.

Lastly, a little spoiler for your next class is also on that site.

-m@rk

## Sunday, April 27, 2008

### Exponents and Logarithms worksheet

Here is another comment regarding Zeph's questions. I really enjoy answering questions. It sorts of review me about everything i learned last year.

Zeph,

Now I'm going to show you how to do question 16. Special credits to benofschool for showing me how to do this.

[log_3(X)]^2 - log_3(x)^2 = 3

Apply the rules of logarithms.

[log_3(x)]^2 - 2log_3(x) = 3

Let, log_3(x)= y

y^2-2y=3

Apply algebraic massage

y^2-2y-3=0

Solve for y.

(y+1) (y-3)=0

y=-1 y=3

Substitute back log_3(x)= y

log_3(x)=-1 and log_3(x)=3

x= 1/3 and 27

I'm going to post the answer for the other questions tomorrow.

-m@rk

Zeph,

Now I'm going to show you how to do question 16. Special credits to benofschool for showing me how to do this.

[log_3(X)]^2 - log_3(x)^2 = 3

Apply the rules of logarithms.

[log_3(x)]^2 - 2log_3(x) = 3

Let, log_3(x)= y

y^2-2y=3

Apply algebraic massage

y^2-2y-3=0

Solve for y.

(y+1) (y-3)=0

y=-1 y=3

Substitute back log_3(x)= y

log_3(x)=-1 and log_3(x)=3

x= 1/3 and 27

I'm going to post the answer for the other questions tomorrow.

-m@rk

### Exponents and Logarithms worksheet

This was my answer regarding Zeph's question. He was asking on how to do a specific question because he was not in class for the whole week because of some extra curricular activity. Here it is.

Zeph,

I'm going to answer your second question first, since it is tougher.

Question 15

logX^2 = (logX)^2

First is to apply the rules for logarithms.The equation will look like this:

2logX= (logX)^2

Now, let logX= y (or some other variable. The equation will look like this:

2y=y^2

Do some algebraic massage

0=2y-y^2

0= y (2-y)

y= 0 and y=2

Now substitute back logX=y

logX=0 and logX=2

Take antilog of both sides

x=10^0 and x=10^2

x=1 and x=100

-m@rk

Zeph,

I'm going to answer your second question first, since it is tougher.

Question 15

logX^2 = (logX)^2

First is to apply the rules for logarithms.The equation will look like this:

2logX= (logX)^2

Now, let logX= y (or some other variable. The equation will look like this:

2y=y^2

Do some algebraic massage

0=2y-y^2

0= y (2-y)

y= 0 and y=2

Now substitute back logX=y

logX=0 and logX=2

Take antilog of both sides

x=10^0 and x=10^2

x=1 and x=100

-m@rk

## Thursday, April 24, 2008

### BOB Version 4: Exponents and Logarithms

This was my comment on Zeph's BOB post. I've finally caught up on my mentoring duties. Again, I apologize, If I'm doing my comments a little late, It is just because that AP exams are just around the corner and its almost crunch time.

Zeph,

Good BOB post! It seems to me that this new format is going to attract more attention. There are more people who are going to imitate this, much like your other format. Over my two years with Mr. K, I've never seen this done before. You are continually proving that math coexist with language. Good luck on the upcoming test.

-m@rk

Zeph,

Good BOB post! It seems to me that this new format is going to attract more attention. There are more people who are going to imitate this, much like your other format. Over my two years with Mr. K, I've never seen this done before. You are continually proving that math coexist with language. Good luck on the upcoming test.

-m@rk

### BOB for Logs

This was the comment I left on Rence's BOB post. It is interesting to see how they are improving as time passes by. This bunch of people are continuing to intrigue me, now I cant wait till Ap exams are over , so i can do some math with this people.

Rence,

I hope that you study hard for the upcoming test.On your BOB post, you mentioned, "Ln (pronounced Ellen..). Apparently it's easier BECAUSE it has ONE LESS LETTER." A clever reason but that is not the case, if you want to know why Ln is widely easier, I think that you should take AP Calculus for next year. You will see that the base e has so many cool properties. I don't want to spoil anything, so I'm going to stop now. Good luck!

-m@rk

Rence,

I hope that you study hard for the upcoming test.On your BOB post, you mentioned, "Ln (pronounced Ellen..). Apparently it's easier BECAUSE it has ONE LESS LETTER." A clever reason but that is not the case, if you want to know why Ln is widely easier, I think that you should take AP Calculus for next year. You will see that the base e has so many cool properties. I don't want to spoil anything, so I'm going to stop now. Good luck!

-m@rk

### "EXPONENTIAL MODELING"

Now that the AP exams is only about three weeks away, I'm starting to forget about my mentoring duties, my apologies. This was my comment on Jamie's scribe post regarding exponential modeling.

Now i just need to do more catching up.

Jamie/PBnJamieSnagwich,

Good scribe post.I like how you modified Zeph's format and you said that "I'm not the one who follows the whole OUTLINE idea, because not everything I write is written in stone". Thats a good move, because not everyone works the same way. People have their own different ways of expressing themselves.

-m@rk

Now i just need to do more catching up.

Jamie/PBnJamieSnagwich,

Good scribe post.I like how you modified Zeph's format and you said that "I'm not the one who follows the whole OUTLINE idea, because not everything I write is written in stone". Thats a good move, because not everyone works the same way. People have their own different ways of expressing themselves.

-m@rk

Labels:
mark,
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### Logarithms and Exponents Practice

After reading some people's reflection on the logarithms and exponents unit, I must say that they are pretty comfortable with the concepts, but i still decided to make a post containing some of the online quizzes that they can use to study and ace the test tomorrow.

I can see that most of you guys are loving this unit, but I still made a collection of online quizzes that can be found around the net.There are many good sites out there that you can practice on, so I decided to make a list of few sites that will definitely help all of you. Here it goes:

Link 1

Link 2

Link 3

Link 4

Link 5

Link 6

Link 7

Link 8

Link 9

Link 10

I planned to post this earlier but my internet connection is acting weird because of the weather outside.

-m@rk

I can see that most of you guys are loving this unit, but I still made a collection of online quizzes that can be found around the net.There are many good sites out there that you can practice on, so I decided to make a list of few sites that will definitely help all of you. Here it goes:

Link 1

Link 2

Link 3

Link 4

Link 5

Link 6

Link 7

Link 8

Link 9

Link 10

I planned to post this earlier but my internet connection is acting weird because of the weather outside.

-m@rk

## Tuesday, April 15, 2008

### Logarithms and Their Laws

This is comment on Joyce's post. Her post was also about logarithmic laws and its application. I must say that I'm loving how they are including images when they are trying to explain a certain concept. It is just easier to learn compare to a scribe post with just plain text.

Joyce,

I must say that it was a really long scribe post, but it was very well done. Like i said on Kristina's scribe post, I like how you inserted an image so that your readers can easily link to what you are saying. It saves them lots of time and most of all makes them learn visually. I like to consider myself as a visual learner so this post really helped me relearn all this laws.

-m@rk

Joyce,

I must say that it was a really long scribe post, but it was very well done. Like i said on Kristina's scribe post, I like how you inserted an image so that your readers can easily link to what you are saying. It saves them lots of time and most of all makes them learn visually. I like to consider myself as a visual learner so this post really helped me relearn all this laws.

-m@rk

### Logarithmic Laws

This is my comment on Kristina's scribe post. Her scribe post was all about logarithmic laws and its applications, so without further ado here it is.

Kristina,

I personally like how you included an image when you were trying to explain the logarithmic laws. It was easier to understand and it save me lots of time because i don't need to scroll back and forth from the slides to your post. Now, i need to relearn all this laws once again.

-m@rk

Kristina,

I personally like how you included an image when you were trying to explain the logarithmic laws. It was easier to understand and it save me lots of time because i don't need to scroll back and forth from the slides to your post. Now, i need to relearn all this laws once again.

-m@rk

### Logarithmic Spiral

Well, after one of the busiest week of my life, this was the only time that I've finally caught up on my mentoring duties and reading, so here was my comment on Richard's scribe post titled "Logarithmic Spiral".

Richard,

Good scribe post. I learned a couple of things from your post. First, I didn't know that snail shells, tornado , spiral galaxies and even Romanesque broccoli grows the same way as the logarithmic spiral. Second, i need to do 2 quizzes tomorrow. Lastly, just a word of advice, you might want to highlight some parts of your scribe post if you are trying to emphasize an important concept.

-m@rk

Richard,

Good scribe post. I learned a couple of things from your post. First, I didn't know that snail shells, tornado , spiral galaxies and even Romanesque broccoli grows the same way as the logarithmic spiral. Second, i need to do 2 quizzes tomorrow. Lastly, just a word of advice, you might want to highlight some parts of your scribe post if you are trying to emphasize an important concept.

-m@rk

## Friday, April 11, 2008

### Solving Exponential Equations + Looking at exponential graphs.

Well, i thought that I would drop by and leave Eleven's post a comment. The post itself was kind of late, because the last time i checked at about 2:00 am , it was not yet published, so without further ado here is my comment.

Eleven,

Its better late than never, eh? Well, I personally like how you structured your scribe post, especially the little side comments at the end of each question and how you use bold letters to emphasize a certain concept. Those are good methods to make the concepts stick in your head. It seems to me that you are really comfortable in what you are doing. Good job!

-m@rk

Eleven,

Its better late than never, eh? Well, I personally like how you structured your scribe post, especially the little side comments at the end of each question and how you use bold letters to emphasize a certain concept. Those are good methods to make the concepts stick in your head. It seems to me that you are really comfortable in what you are doing. Good job!

-m@rk

## Monday, April 7, 2008

### FLick Off

Well, now that I'm on top of my todo list (thanks to the week long break). I decided to continue my mentoring chore, so this was my comment on PBnJamieSnagwich's post.

PBnJamieSnagwich,

I'm sure that Mr. K will look at your suggestion of grouping all your flickr photos into just one place so it can be accessible in just one click. This ca be very useful if you want to use the flickr images to study. I really think that it is a clever idea.

BTW, I watched the movie, 21 too. I really think that it was very clever, but i don't recommend that you guys should go gambling. I wonder if Mr. K will use the movie when you guys study the unit of probability.

-m@rk

PBnJamieSnagwich,

I'm sure that Mr. K will look at your suggestion of grouping all your flickr photos into just one place so it can be accessible in just one click. This ca be very useful if you want to use the flickr images to study. I really think that it is a clever idea.

BTW, I watched the movie, 21 too. I really think that it was very clever, but i don't recommend that you guys should go gambling. I wonder if Mr. K will use the movie when you guys study the unit of probability.

-m@rk

## Sunday, April 6, 2008

### Sum and difference identities

This was my comment concerning this specific identity. I personally detest long formulas but this one is very useful and easy to remember.

A very well detailed scribe post. This scribe post helped me remember the concept behind this specific identity. I remember the fist time that i learned this identity, i found it really dry and boring. Now, i just need to put this found knowledge in the upcoming test. Keep up the good work!

-m@rk

Also, another comment concerning the same matter.

Anhthi,

Good scribe post. This scribe post sort of reminded me of the JABBAWOCKEEZ because of the way that you use kinesthetics to learn the sum and difference identities. Next year, if you take Calculus with Mr. K you guys will not just dance but also sing. Also, about that superstition about writing your name in red ink, my friend said that it doesn't mean anything important. Keep up the good work!

-m@rk

A very well detailed scribe post. This scribe post helped me remember the concept behind this specific identity. I remember the fist time that i learned this identity, i found it really dry and boring. Now, i just need to put this found knowledge in the upcoming test. Keep up the good work!

-m@rk

Also, another comment concerning the same matter.

Anhthi,

Good scribe post. This scribe post sort of reminded me of the JABBAWOCKEEZ because of the way that you use kinesthetics to learn the sum and difference identities. Next year, if you take Calculus with Mr. K you guys will not just dance but also sing. Also, about that superstition about writing your name in red ink, my friend said that it doesn't mean anything important. Keep up the good work!

-m@rk

### Just a little help...

I remember when i made this post i was going over their BOBs and i was starting to see the same pattern that everyone still need a little bit of practice about trigonometric identities for the upcoming test.

I can see that most of you guys are having some trouble with trigonometric identities. The only way that you can be good at it is by doing some practice questions, so you can develop a knack on seeing the patterns in this mini mind puzzles. There are many good sites out there that you can practice on, so I decided to make a list of few sites that will definitely help all of you. Here it goes:

http://library.thinkquest.org/20991/alg2/trigi.html#Quiz

http://www.syvum.com/cgi/online/serve.cgi/math/trigo/trig2.tdf?0

http://www.quia.com/cc/448321.html

http://www.epcc.edu/Student/Tutorial/Mathcenter/Exams/trigquizzes/quiz14/QUIZ14.htm

http://www.libraryofmath.com/trigonometric-identities-quiz.html

http://www.batesville.k12.in.us/physics/CalcNet/Trig_Review/Trig_Review.html

http://college.hmco.com/cgi-bin/SaCGI.cgi/ace1app.cgi?FNC=AcePresent__Apresent_html___mathematics_larson_algebra_trig_6e_07-02

-m@rk

I can see that most of you guys are having some trouble with trigonometric identities. The only way that you can be good at it is by doing some practice questions, so you can develop a knack on seeing the patterns in this mini mind puzzles. There are many good sites out there that you can practice on, so I decided to make a list of few sites that will definitely help all of you. Here it goes:

http://library.thinkquest.org/20991/alg2/trigi.html#Quiz

http://www.syvum.com/cgi/online/serve.cgi/math/trigo/trig2.tdf?0

http://www.quia.com/cc/448321.html

http://www.epcc.edu/Student/Tutorial/Mathcenter/Exams/trigquizzes/quiz14/QUIZ14.htm

http://www.libraryofmath.com/trigonometric-identities-quiz.html

http://www.batesville.k12.in.us/physics/CalcNet/Trig_Review/Trig_Review.html

http://college.hmco.com/cgi-bin/SaCGI.cgi/ace1app.cgi?FNC=AcePresent__Apresent_html___mathematics_larson_algebra_trig_6e_07-02

-m@rk

### Pythagorean Identitties

This is my comment to Zeph. I was clearly intrigue by the format of his scribe. I wish my mind works sequentially and clearly as his post.

Zeph,

I should say that I'm really impressed by this post. This post is very well written and organized. I like how you make outlines, it sort of summarized everything that happened in class. Keep up the good work!

-m@rk

Zeph,

I should say that I'm really impressed by this post. This post is very well written and organized. I like how you make outlines, it sort of summarized everything that happened in class. Keep up the good work!

-m@rk

### Word problems

I know that i should have posted this a long time ago, but this past month has been a killer for me. Well, it was a good test of time management and mental toughness though so without further ado, here's one of the comments i made a month ago:

After doing the whole question by myself, I must say that this is the most challenging question among the bunch. It took me about 35 minutes and a lot of coffee. I think that you have the arrow of the wave on the left of the x-axis on the right position contrary to what other people say. Good luck on the upcoming test.

-m@rk

Also, i made another comment on the same assignment from a different group:

Paul,

I think you made a good point. I also think that the amplitude should be 20 because the ferris wheel is 1 meter above the ground.That being said the vertical shift will change too,it will be 21. Like you said it is a matter of one's interpretation. Now, i kinda like to go to class once in a while to see the class's progress but too bad i still have my AP class.

-m@rk

After doing the whole question by myself, I must say that this is the most challenging question among the bunch. It took me about 35 minutes and a lot of coffee. I think that you have the arrow of the wave on the left of the x-axis on the right position contrary to what other people say. Good luck on the upcoming test.

-m@rk

Also, i made another comment on the same assignment from a different group:

Paul,

I think you made a good point. I also think that the amplitude should be 20 because the ferris wheel is 1 meter above the ground.That being said the vertical shift will change too,it will be 21. Like you said it is a matter of one's interpretation. Now, i kinda like to go to class once in a while to see the class's progress but too bad i still have my AP class.

-m@rk

## Thursday, March 13, 2008

### Mathematical Modelling

While i was doing my daily routine of reading the blog, I've seen some homework that were posted by my peers. I should say that I'm quite impress by the quality of their work. I'm starting to really like this bunch of people. I can see that they are really enthusiastic to learn math. Now, i kinda want to go to the class and meet all of them, so i left their homework some comments.

First of all good job on the detailed answer. I really like how you put a lot of space so your solution will be easy to follow.After doing the whole question myself, I therefore conclude that Zeph's answer is the right one. There is something wrong with the algebra. There are many different ways to check this problem. One of them is to use your calculator. First of all, you need to plug in the function. Then press the 2ND button then TRACE then press 1.After that plug in your answer as the x value then press ENTER. You should see that the y value should be very close to 4. Thats the quick way of doing it.

-m@rk

Here's another comment from another homework.

Great work everyone! I really like that your solution is easy to follow because of the added space. After checking your solutions, I therefore conclude that it is perfect. Now, I just need to check two more questions from the other groups.

-m@rk

First of all good job on the detailed answer. I really like how you put a lot of space so your solution will be easy to follow.After doing the whole question myself, I therefore conclude that Zeph's answer is the right one. There is something wrong with the algebra. There are many different ways to check this problem. One of them is to use your calculator. First of all, you need to plug in the function. Then press the 2ND button then TRACE then press 1.After that plug in your answer as the x value then press ENTER. You should see that the y value should be very close to 4. Thats the quick way of doing it.

-m@rk

Here's another comment from another homework.

Great work everyone! I really like that your solution is easy to follow because of the added space. After checking your solutions, I therefore conclude that it is perfect. Now, I just need to check two more questions from the other groups.

-m@rk

## Tuesday, March 11, 2008

### Critical Thinking

While I was surfing through the blog, I noticed that most of the post were talking about Mr. K's new gimmick of making his students think. His new gimmick is to tell one lie per day so that his students will critically analyze everything that he says. This method sorta reminds me of this blog post that i read on one of the blogs on my rss feeds. The post talks about another teacher that uses the same methodology to make his students pay more close attention to what he is saying.

Zeph,

I'm quite impress that you caught that lie. I didn't even caught that one when i was trying to redo the whole question by myself. It's quite nice to see that many of you guys are getting a lot from Mr. K's lies. I guess that his strategy makes all of you critical analyze what he is saying.Good job and keep up the good work!

-m@rk

Zeph,

I'm quite impress that you caught that lie. I didn't even caught that one when i was trying to redo the whole question by myself. It's quite nice to see that many of you guys are getting a lot from Mr. K's lies. I guess that his strategy makes all of you critical analyze what he is saying.Good job and keep up the good work!

-m@rk

## Tuesday, February 26, 2008

### Trigonometric Equations

While I was checking the blog for more questions to answer, I stumbled upon one of my classmates questions. This question is about trigonometric equations, so here was my response:

Benofschool,

Good job for trying to look for the answers. Your hard work only shows how dedicated you are to this class and how much effort you give into it.

Unfortunately, i don't think the answers are right.

Let's examine the first question first.

cos(2x)=1/2

Think of this as your regular algebra question. You can see that the only thing that is in your way is the cosine, so what you have to do is use arccos on both side to get rid of the cosine. That will leave you with this:

2x= 1.0472

Then with some more algebra you will get:

x= 0.5236 + kpi

AND the other other angle at quadrant 4 which is 2.6180 +kpi

Another way to solve this is to use the exact values of the unit circle.

cos2x= 1/2

We know that the cosine of 1/2 is pi/3, so that will leave you with this:

2x=pi/3

Now, again solving for x with some algebra we will get this:

x=pi/6+ kpi

AND

the other angle at quadrant 4 which is 5pi/6 +kpi

Im gonna let you finish up the next question. Hopefully that helps you in some way.

-m@rk

Benofschool,

Good job for trying to look for the answers. Your hard work only shows how dedicated you are to this class and how much effort you give into it.

Unfortunately, i don't think the answers are right.

Let's examine the first question first.

cos(2x)=1/2

Think of this as your regular algebra question. You can see that the only thing that is in your way is the cosine, so what you have to do is use arccos on both side to get rid of the cosine. That will leave you with this:

2x= 1.0472

Then with some more algebra you will get:

x= 0.5236 + kpi

AND the other other angle at quadrant 4 which is 2.6180 +kpi

Another way to solve this is to use the exact values of the unit circle.

cos2x= 1/2

We know that the cosine of 1/2 is pi/3, so that will leave you with this:

2x=pi/3

Now, again solving for x with some algebra we will get this:

x=pi/6+ kpi

AND

the other angle at quadrant 4 which is 5pi/6 +kpi

Im gonna let you finish up the next question. Hopefully that helps you in some way.

-m@rk

## Monday, February 25, 2008

### Tangent Function

Second post on my mentoring blog.While I was doing my regular routine of reading our blog the most common thing that i see people have problems with is the,tangent function. Anyways,what is the tangent function? It's time to put my thinking cap on and help my fellow classmates with this.

Zeph,

As for your other question. The graph of the tangent function can be viewed here: http://fooplot.com/index.php?q0=tan(x)

The tangent function has some cool properties. It has an amplitude of undefined, a period of pi and y intercept of zero.

I have so much more to say but i don`t want to spoil the fun.

-mark

Also, I've seen a similar question from Roxanne, so i decided to give her some insights about the tangent function. I gave her more details.

Roxanne,

If you want to see the graph of the tangent function, you can go right ahead and use fooplot.com. You will see that the shape of the tangent function is somewhat different from cosine and sine.

The graph of the tangent function has some distinct properties.It has a period of pi unlike both cosine and sine which has a period of 2pi.

Second, it has a y-intercept of zero. (There are so much more to say about this function but i wont go into them, because i don't want to spoil the fun).

Graphing the tangent function follows the same rule as graphing both cosine and sine functions. The general equation for the tangent function is f(x) = a*tan(bx+c)+d. You can see that it uses the same parameters.All the parameters work the same way as the one in the sine and cosine equations. It also follows the same algorithm DABC (but i prefer using BCDA).

I hope this helps you clarify things.

-m@rk

Zeph,

As for your other question. The graph of the tangent function can be viewed here: http://fooplot.com/index.php?q0=tan(x)

The tangent function has some cool properties. It has an amplitude of undefined, a period of pi and y intercept of zero.

I have so much more to say but i don`t want to spoil the fun.

-mark

Also, I've seen a similar question from Roxanne, so i decided to give her some insights about the tangent function. I gave her more details.

Roxanne,

If you want to see the graph of the tangent function, you can go right ahead and use fooplot.com. You will see that the shape of the tangent function is somewhat different from cosine and sine.

The graph of the tangent function has some distinct properties.It has a period of pi unlike both cosine and sine which has a period of 2pi.

Second, it has a y-intercept of zero. (There are so much more to say about this function but i wont go into them, because i don't want to spoil the fun).

Graphing the tangent function follows the same rule as graphing both cosine and sine functions. The general equation for the tangent function is f(x) = a*tan(bx+c)+d. You can see that it uses the same parameters.All the parameters work the same way as the one in the sine and cosine equations. It also follows the same algorithm DABC (but i prefer using BCDA).

I hope this helps you clarify things.

-m@rk

### Function Notation

First post on my mentoring blog. Kind of weird trying to help my fellow classmates in their math studies based on my experiences and wisdom that I gained from taking this class last year.

Zeph,

Question #15 on exercise 2 is just simply using function notation. Since f (x) = 2x + 3 and you have to find k so that f(k+2) = k + f(k).

so we`ll work on the right side first, all you have to do is just substitute k+2 to x so you have:

2(k+2) + 3

On the other side since k is just a constant you just leave it and then again reading the function notation you need to substitute k to x so you have this:

k+ 2(K)+3

Therefore, you will end up with this kind of equation:

2(k+2) + 3 = k + 2k + 3

Then with the help of some algebra you will get this answer:

2k + 7 = 3k + 3

4 = k

-mark

Zeph,

Question #15 on exercise 2 is just simply using function notation. Since f (x) = 2x + 3 and you have to find k so that f(k+2) = k + f(k).

so we`ll work on the right side first, all you have to do is just substitute k+2 to x so you have:

2(k+2) + 3

On the other side since k is just a constant you just leave it and then again reading the function notation you need to substitute k to x so you have this:

k+ 2(K)+3

Therefore, you will end up with this kind of equation:

2(k+2) + 3 = k + 2k + 3

Then with the help of some algebra you will get this answer:

2k + 7 = 3k + 3

4 = k

-mark

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