Station 3. Round and Round We Go.

In this station we compared various graphs with Sine, Cosine, and Tangent by using an interactive Ferris Wheel as the unit circle. The interactive allowed you to compare the three graphs and to see them in motion so you could see how each degree was different in comparison to each radian to each graph: Sine, Cosine, and Tangent.


http://www.andrewbusch.us/uploads/1/5/1/2/15122632/9561526_orig.png 

Station 2. Radians Vs. Radius...

In this station we learned that one standard radian is the equivalent of the radius on the unit circle. We compared the length of the radius with a pipe cleaner to the arch length and marked the end of that pipe cleaner to indicate the terminal or other side of the angle. That angle was the equivalent of one radian. In the end we discovered that 6 radians fit into a circle evenly with a little of a quarter of a radius left over.



http://courseware.cemc.uwaterloo.ca/8/163/assignments/91


http://zonalandeducation.com/mmts/trigonometryRealms/radianDemo1/RadianDemo1.html

Station 5. Standard Position on the Unit Circle

We learned that standard position always begins on the right x axis side. With this interactive we also observed which angle measures lied in which quadrants. We also learned that a quadrantal angle is when the terminal side (or where the angle measure ends) ends up on an x or y axis.


http://laddlincolnguevarra.tumblr.com/post/107075551402/angles-in-standard-position



http://www.pinkmonkey.com/studyguides/subjects/trig/chap2/t0202206.asp

Standard Position

Station #5

In this activity I learned about angles in standard position.  An angle is in standard position if it's vertex is on the origin and one ray (initial side) is located on the positive x-axis.  The initial side is the one on the x-axis, while the terminal side can move.  If the terminal side lies on one of the axes than an angle is considered a quadrantal angle.

What is a radian???

What is it?!

Station #2

In this activity we explored into the world of a circle.  We learned that a radian is an angle equal to a circle's radius.   In the picture you can see this.  I enjoyed this activity because it was interactive and consisted of creating what is seen below.   

station 2- Briar Edgerly

This is station 2. In this station you used the radius and compared it to the circle.

Overview w/ E Whales

This is a picture of what our sheet looked like to keep track of all of our stations. We got cool stickers when we did our work and that was very motivating. On this sheet, you can see Station #1 on it and that was a cool station because we got to see where some of the math we were learning about was used in the real world. We looked at a couple different websites to see where in the world we could use math like this. It was kind of neat. 


This is a picture of me and Summer having a grand ole time in math. We really enjoyed these stations because we love learning and we love PreCalc. Go math! 


I thought that this picture was cool because we are learning a lot about pie and such. 

Station 1- Briar Edgerly

This is station one. In this station trig was talked about. The station showed how trig is used and what real life careers it is used in.

Station 2 by E Whales

Station 2- What is a radian?



In this station, we learned what a radian was. I had never really heard of a radian before, so it was neat to learn about. I learned that a radian is the angle that has an arc length equal to the radius of the circle. I also learned that 1 radian = about 60 degrees. This station was very interactive and hands on, which made it easier to learn and understand.

Station #2

At Station #2 we figured out what a radian was. We started by picking up our materials (paper, lid, markers, pipe cleaner, scissors, ruler, protractor and glue). We traced the shape of the lid onto a piece of paper and cut it out. We then folded it in half twice and made a dot in the center with a marker. After that we took the pipe cleaner, cut it to the length between the center dot and the edge of the circle, and used the ruler to draw a straight line from the center out to the edge of the circle. We then used the pipe cleaner to measure around the outside of the circle. Each time we came to the end of the pipe cleaner we would make a mark and move the pipe cleaners other end to that dot, moving around the circle. Once we went all the way around, we used the ruler and the marker to make straight lines from the center to the outside of the circle where the dots measuring the end of the pipe cleaner were located. There were six full sections and one small section. We glued the circle to a piece of paper and then the pipe cleaner to one of the lines we had created. We then used the protractor to measure the angle of one of the radians, assuming the others would be approximately the same.

-Emma

Station #3

At Station #3 we investigated two different applets and drew what they looked like on a piece of paper. The first one was a model of a ferris wheel that helped to understand the unit circle. This is the information I drew on my paper:

The next applet showed you what pattern the sine, cosine, and tangent functions followed on a graph. You could select each of the functions individually or see what they looked like all together.

-Emma

Station 3: Summer

STATION 3

While doing trigonometry stations during the past couple weeks station 3 was also one of the more helpful stations. 

In this station I explored a website and got to look at what different graphs look like for sine, cosine, and tangent. I learned a lot at this station because I didn't know that sine, cosine, and tangent were something that could be identified by graphs. The picture above shows what each looks like on a graph.  The sine and cosine graphs are somewhat similar while the tangent graph is extremely different.

Station 5: Summer

STATION 5

While doing trigonometry in Pre-Calc last week station 5 helped me make a useful resource that has to do with angles in the standard position.

At Station 5 there were materials there for us to make this resource as well as another paper for us to put more notes on and for practice to make sure that we understood the concept of standard position angles. Above you will find a picture of my work at this station along with another picture of more notes I took along with some practice.

Station 2: Summer

STATION 2

While doing Trigonometry stations in class these past couple weeks, station 2 was one of my favorites due to it being more hands on.

In station 2 we all learned what a radian was by tracing a circle on a paper and labeling the radians within it with a pipecleaner the length of the radius of the circle that was traced. I learned that about 6 radians could fit within the circle I traced and that each radian equals about 60 degrees.

Station 3 by E-Whales

Station 3- 



In this station, we had to go on the internet and look at the difference in the graphs between sine, cosine, and tangent. I learned a lot because before this station I really had no clue what the graphs would look like. I learned that the sine starts at 0, the cosine starts above (at 1), and the tangent has three weird lines running through it.

The above image shows my sketches from that station.

Station 4

-Matt
In station 4 I went on to instagrok which is that website with the weird web looking thing. Anyways I I learned about the unit circle and a key fact that I saw was that the quadrants of the unit circle make up a trigonometric graph. Also I watched videos and saw images of the unit circle. The unit circle is a circle with a radius of one and is centered on the origin. 

Station 5

In Station 5 I used my arts and craft skills to make a spinner that helped me draw angles in Standard Position.

This is the spinner that I made.

If the terminal side arrow is moving counter-clockwise then the angle will be positive. If the terminal side arrow is moving clockwise then the angle will be negative.

I also watched a video that helped me understand how to draw the angles. The degrees in the quadrants really helped me when I was working on the worksheet, so I could see where the terminal side would be placed.

Station 3

In Station 3, I used the two applets to make graphs of sin, cosine, and tangent. The first link was a ferris wheel that modeled a unit circle. You could make the sin graph by tracking the blue seat as it went around the ferris wheel. On the second link, you could layer the different graphs of sin, cosine, and tangent together to compare and contrast them. All three looked very different to me.

This is a picture of what the diagram looked like on the second applet.

Station 2

In Station 2, I made a diagram that shows what a radian is. I used a pipe cleaner to trace around a circle to show how many radians fit in the circle. A little more than 6 radians fit in a circle.
1 Radian = approx. 60 degrees.

This is a picture of the circle I created.

Station #5

At Station #5 we learned about standard positions. We followed the instructions to make the interactive model shown below. 

We cut out the arrows, glued one onto the sheet of paper and attached the other to make it spin around. We then watched videos or read information about different positions. While watching a video, I traced the movable arrow in some of the positions I saw on the video, so I could add some extra information that I would not put on the other sheet and to help with my understanding. We also answered the questions on the bottom of the colored paper. 

After watching a video and looking through another site, I filled out the top of the “Sketching Angles in Standard Position” form. I then sketched the positions of the other angles at the bottom and checked those answers.

-Emma

Station 5

-Matt
In Station 5 we learned about standard positions and angles and again we did more crafts and created a spiny wheel thing that shows the terminal side and initial sides and what makes angles positive and negative. An angle is in standard position if it's vertex is located on the origin and one ray is located on the positive x axis.

Station 4- Trig and the Unit Circle

Station 4 was a online, interactive website that taught about the Unit Circle.  A unit circle is a circle with a radius of one.  Sine, Cosine and Tangent are used.


  

This is brennan. He is math.

Station 2

- Matt
In station 2 we began to learn about the radian and radius of circles.  A radian is an angle that has arch length equal to the radius to the circle.  So we took the time to do some crafts to demonstrate what the radius and radian are. I cut out a circle and took the radius with a pipe cleaner than measured all the way around the circle with the cleaner giving me the radian. One radian is approximately 59 degrees.

Investigate Instagrok on Trigonometry and the Unit Cirlce

In this station, there was a lot of facts about the unit circle, including some key facts like that the unit circle is the source of the generation of the trigonometric function graphs. There are also some websites to help with some more help with these. There are also some images and videos that you can watch for more help.

Graphs of Trigonometric Functions

In this station, you had to show the graph of sin, cosine and tangent.

This is basically it.

Online Investigation

In this station, I chose to look at "Fire Away" and "Fascinating Facts About Math"

From these, I learned how people use trig to find the trajectory of a missile (or a missile like object) and some really cool facts, like that they use trig in planes so that the planes know where to go. 

Today in class, we learned how to apply the Change of Base Formula of logarithms. It was so very fun. We also learned how to solve logarithmic and exponential equations when bases are different. That was a blast as well. 

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Here is some of the easier stuff first…

log89= log 9/log 8

When you type that into the calculator you put in…

log(9) / log(8) 

Make sure you have the parenthesis! 

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Now the harder stuff…

2^4x-1 = 3^1-x

1) Bring the parenthesis down in front

 

2) Apply (log) to each of the numbers

It should look like this…

(4x-1)(log2)=(1-x)(log3)

3) Next, Distribute

4x(log2) - 1(log2) = 1(log3) -x(log3)

4) Then, combine the like terms

4x(log2) + x(log3) = log3 + log2

5) After that, factor out the x

x (4log2 + log3) = log3 + log2

6) Divide to get the x by itself (use calculator)

x = log3 + log2 / 4log2 + log3

7) The answer should be x= .977!

http://logarithmicandexponential.weebly.com/math-memes.html

Monday Math (Monday April, 4)

Today in class we practiced the properties and laws of logarithms.  We did a warmup with all examples of condensing and expanding logarithms.  We then did another worksheet on expanding logarithms before we went on to work on IXL.

We need to have IXL's R8, R9, and R10 up to a 70 and R11 up a 90 before Fridays test.  

This is a question on R11.  This log needs to be expanded using the quotient and power law.
8logx y - logxW would be the answer.

In class 3/28/16

In class, we finished our notes on logarithmic functions. In our notes we learned what "e" is (e=2.7182818284509...). We compared "e" to pi and learned how to use "e" in an equation. After finishing our notes, we did some practice problems that had to do with what we had just learned in our notes. We were also assigned two IXL's. These are my copies of the notes and the practice problems.

Notes:

Practice Problems:

3-29-16 Tuesday bisquits

Today in class we basically just reviewed for our test. Math Math Math Math Math Math Math Math

 Math Math Math Math Math Math Math Math Math Math Math Math Math Math Math Math Math Math Math MathMath Math Math MathMath Math Math MathMath Math Math MathMath Math Math Math

3/23/16

Objectives of Today's Class: 
Investigate logarithmic functions 

-a logarithmic functions is the inverse of an exponential function


http://www.sosmath.com/algebra/logs/log4/log4.html

(see Summer's post for information on the first side of the notes)

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THE SECOND PAGE OF NOTES…

First, we evaluated how to apply logarithms. Some examples included…

a) log39
To do this problem, you can rewrite it as 3^x=9 and then you just have to figure out what number goes in for x. In this case, x would equal 2 because 3 squared equals 9. This is one of the simpler problems. Now for a more difficult problem…

d) log48
Write it as 4^x=8. Then, you make the bases equal. In this case, we can set them as 2. So it would look like 2^2x=2^3. Then you would set up the exponents like an algebra problem and solve. So, 2x=3, divide 2 on each side and you get that x= 2/3. 

Second, we looked at common logs and how to solve/evaluate them. For example…

log 100 would equal 2 because 10 squared equals 100

log 1 would equal 0 because the only power that 10 could go to to equal 1 is 0

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Remember…

Common log= log base 10 

10^x=y is the same thing as log10y=x 

Ask yourself: 10 to what power will give you x?

Class Wed. 3/23 & Symbaloo

3/23/16

At the beginning of class (the first 15 minutes) we got the chance to record about one color of the symbaloo links we are doing about logarithms. In case you missed it, we are going to be taking the first few minutes of class to do one color, and one is going to have to be done over the weekend. The grade is going to go in Wednesday of next week as a small quiz grade. Below is one of the symbaloo links researched. 

After that, we did notes on investigating logarithmic functions. Mrs. Hatfield made an analogy that an logarithm is like translating English to Spanish and Spanish to English. You take the reflection of the equation. Logarithms they are inverses that reverse the process. With them being inverses the domains and ranges switch and one asymptote.

  

Please see Erin's blogpost for the second page of notes! :)

In class tuesday, we learned about the real life implications of logarithms. We watched a video about the power of tens that showed how massive our universe is! We then had to find real life examples of where logarithms are used.

One example that I found was decibels.

3/22/16

In class on Tuesday, March 22 we were introduced to logarithms.  We watched a mind-blowing video called "The Powers of Ten" (https://www.youtube.com/watch?v=0fKBhvDjuy0&noredirect=).



After that we researched real world examples of logarithms.  One I researched was about The Richter Scale that is used to measure earthquakes.

Today, (By today, I mean 3/21/16) we did some practicing with logarithmic equations with like bases. This picture shows a good example on how to navigate what to do if you have multiply your exponents.

Stations

Apparently I never posted about the stations we did when we first started regressions and exponential decay and growth, and got it put in as a missing grade, as a result, I am posting about it now. 

On week 1 we were introduced to exponential decay and growth. To educate us about these topics we went to 4 out of 5 stations to begin. Each station went over something different. 

Every student got to choose between station 1 and station 5. I chose the stations as followed:
- Station 2: M&M Activity: Fish Population Lab: Exponential Decay/Growth Activity.
- Station 3: April Showers Bring May Flowers
- Station 4: Exponential Applet Investigations
- Station 5: Investigate Instagrok on Exponential Functions

Each station had learning goals and when we were done we got stamps.

We now have a better understanding of exponential decay and growth due to these stations!