lol Hey Everyone
Well this unit has practically zoomed by and, for me, has been the easiest unit of them all. It was made especially easy by the fact that there were only a very small number of formulas to memorize and a lot of graphs and patterns. The only thing I really need to remember for these is how to find the focuses on ellipses and how to graph a hyperbola.
Ellipses
take the square root of the difference between the semi-major axis squared and the semi-minor axis squared. this is how far, along the major axis, the foci's are from the center.
Hyperbola
first you need to draw the box created by the conjugate and semi transverse axises. from there you can draw the diagonal lines that make up the asymptotes of the hyperbola. Each one intersects the two opposite points on this box that has been created. Now take the lengths of the conjugate axis and the semi-transverse axis. Now square both of them and add them together. Then take the square root of that to find the distance between the centre and one of the foci's.
Well that is practically everything that I can think of at the moment so Wish Me Luck!!
See you guys in class.
Jessi
Showing posts with label Jessi. Show all posts
Showing posts with label Jessi. Show all posts
Sunday, May 31, 2009
Tuesday, May 19, 2009
CoNiCs!!!!! go Mitsubishi Honda Civic!!!!!
Hey everyone, Jessi here. Welcome officially to the last month of school. Well now to get down to business.
Very first thing in class Mr. K introduced his split personality, the Samurai Mitsubishi Honda Civic. Well this very interesting individual was there to teach us all about the mystical ways of the CONIC ARTS.
1) if you take a line and spin it you create a double napped cone.
2) if you take the cone created and cut it across the top, parallel to the base, the cross section is a circle.
3) if you take the cone again and cut it across at an angle it creates an ellipse.
4) once again take the cone and cut it at an angle, cutting down to the base. The cross section of the shape created is a parabola.
5) lastly cut the double napped cone and cut it perpendicular to the base. This creates a hyperbola
Once we finished that, Mr. K had us put a dot on anywhere on in the bottom quarter of a piece of paper. We placed dashes on the edge of the paper which we then folded over to touch the dot. By doing about ten of these dashes, we found that the crease created by the folds made a parabola. We then placed a dot anywhere on the curve of the parabola. It was found that this dot was the same distance from the first dot we put on the paper and the edge of the paper. This means that a parabola is the locus of points that are of an equal distance from a fixed point and a line.
When we discussed it we found the almost all of the points on a parabola have a corresponding point which is the same distance from the focus as it. There is only one that does not. This is because it is on the vertex of the parabola meaning that it is exactly half way between the focus and the directrix. The distance between the vertex and the directix or the vertex and the focus is the same and is notated as p. This makes the equation of the directrix k-p if k is the x value of the vertex. This would also make the focus's x value equal to k+p.
Therefore
since the line between P and F is equally to the line between P and D then
This means that the equation for a parabola is
Because of this the equation
is equal to the equation
this means that 4p is equal to 1/a
Well that's really all that we covered...yesterdayI guess lol. Sorry for the late post everyone. See you guys in class soon.
Oh and the scribe for tommorow is...... trinhn92!!!
Very first thing in class Mr. K introduced his split personality, the Samurai Mitsubishi Honda Civic. Well this very interesting individual was there to teach us all about the mystical ways of the CONIC ARTS.
1) if you take a line and spin it you create a double napped cone.
2) if you take the cone created and cut it across the top, parallel to the base, the cross section is a circle.
3) if you take the cone again and cut it across at an angle it creates an ellipse.
4) once again take the cone and cut it at an angle, cutting down to the base. The cross section of the shape created is a parabola.
5) lastly cut the double napped cone and cut it perpendicular to the base. This creates a hyperbola
Once we finished that, Mr. K had us put a dot on anywhere on in the bottom quarter of a piece of paper. We placed dashes on the edge of the paper which we then folded over to touch the dot. By doing about ten of these dashes, we found that the crease created by the folds made a parabola. We then placed a dot anywhere on the curve of the parabola. It was found that this dot was the same distance from the first dot we put on the paper and the edge of the paper. This means that a parabola is the locus of points that are of an equal distance from a fixed point and a line.
When we discussed it we found the almost all of the points on a parabola have a corresponding point which is the same distance from the focus as it. There is only one that does not. This is because it is on the vertex of the parabola meaning that it is exactly half way between the focus and the directrix. The distance between the vertex and the directix or the vertex and the focus is the same and is notated as p. This makes the equation of the directrix k-p if k is the x value of the vertex. This would also make the focus's x value equal to k+p.
Therefore
since the line between P and F is equally to the line between P and D then
This means that the equation for a parabola is
this means that 4p is equal to 1/a
Well that's really all that we covered...yesterdayI guess lol. Sorry for the late post everyone. See you guys in class soon.
Oh and the scribe for tommorow is...... trinhn92!!!
Sunday, May 3, 2009
Hello again Bob!!!
Hey everybody
Well this is probably the test I'm going to have the most trouble with because of the week of class that I missed because of the university thing. The unit seems pretty easy though and I'm fairly confident I understand what has happened since I've been missing so I will probably do alright. I am also now SOOOO thankful for both scribe posts and bobs because that is the only reason I understand what I do. The only thing I'm really worried about is word problems because I wasn't in class to learn how to do them. Well there's not much else I can say that hasn't already been said so I'll see everyone tomorrow. Bye.
Well this is probably the test I'm going to have the most trouble with because of the week of class that I missed because of the university thing. The unit seems pretty easy though and I'm fairly confident I understand what has happened since I've been missing so I will probably do alright. I am also now SOOOO thankful for both scribe posts and bobs because that is the only reason I understand what I do. The only thing I'm really worried about is word problems because I wasn't in class to learn how to do them. Well there's not much else I can say that hasn't already been said so I'll see everyone tomorrow. Bye.
Sunday, April 19, 2009
Our Awesome DEV Timeline
April 25- have first question finished and polished
May 2- have second question finished and polished
May 9- have third question finished and polished
May 16- have fourth question finished and polished
May 23- have fifth question finished and polished
DUE DATE: June 4
May 2- have second question finished and polished
May 9- have third question finished and polished
May 16- have fourth question finished and polished
May 23- have fifth question finished and polished
DUE DATE: June 4
Thursday, April 9, 2009
Bobbing!!!!!!
Hey everybody
Well i found this to be a pretty easy unit over all. The only part that I sometimes have trouble with is finding the "Good Idea" to verify the equations. That and making silly errors and just not catching them. The dance was hilarious and pretty weird but at least I can remember what to do with cos(x +y), cos(x-y), sin(x+y), and sin(x-y). Now it's just having more practice to making it even easier.
I can't believe the semester is pretty much HALF over!!! where did the time go?
Well anyways, see you guys in Precal and good luck on the test.
-Jessi
Well i found this to be a pretty easy unit over all. The only part that I sometimes have trouble with is finding the "Good Idea" to verify the equations. That and making silly errors and just not catching them. The dance was hilarious and pretty weird but at least I can remember what to do with cos(x +y), cos(x-y), sin(x+y), and sin(x-y). Now it's just having more practice to making it even easier.
I can't believe the semester is pretty much HALF over!!! where did the time go?
Well anyways, see you guys in Precal and good luck on the test.
-Jessi
Thursday, March 19, 2009
Yay Identities!!!!!
Hey everyone
Well to start off class today, Mr.K wanted to talk about the "Blogger Hall Of FAME!!". We took a few votes on the subject and here's what we decided:
1) It takes a MINIMUM of 12 votes to get your blog into the blogger hall of fame.
2) NO anonymous votes.
3) NO voting for yourself.
Once we were done with our little bit of classroom democracy, we split up into groups to work on some practice problems. Once we were in our groups, we did a little recap on Pythagorean identities. Remember:
As practice, we simplified a few simple expressions using Pythagorean identities when we could.
Example #1
1) first change the expression to only use sine, cosine, or 1
2) this leaves you with two fractions with the same denominator. Rewrite the expression
3) since the numerator is a pythagorean identity, we now know that the numerator is equal to sin^2 t
4) the numerator and denominator can be factored and the answer that is left over is 1
Once we had finished simplifying the expressions, we found that two of the expressions simplified to the same thing, in this case 1. We used them to write the equation
To check if this is true there are a few strategies that we could use. These are:
1) Work with the more complicated side of the identity first
2) Rewrite both sides using sine and cosine
3) Use a Pythagorean identity
4) Simplify complex fractions or rewrite them
5) Use factoring (especially to create differences of squares)
A very important thing to remember when proving trigonometric identities is that you have to drop down "The Great Wall of China" and you can NOT cross it. This is because, when proving an equation, there is no way of knowing whether or not it is true.
So now that we have covered proving trigonometric identities, on to a new subject!!
Well to start off class today, Mr.K wanted to talk about the "Blogger Hall Of FAME!!". We took a few votes on the subject and here's what we decided:
1) It takes a MINIMUM of 12 votes to get your blog into the blogger hall of fame.
2) NO anonymous votes.
3) NO voting for yourself.
Once we were done with our little bit of classroom democracy, we split up into groups to work on some practice problems. Once we were in our groups, we did a little recap on Pythagorean identities. Remember:
As practice, we simplified a few simple expressions using Pythagorean identities when we could.
Example #1
1) first change the expression to only use sine, cosine, or 1
2) this leaves you with two fractions with the same denominator. Rewrite the expression
4) the numerator and denominator can be factored and the answer that is left over is 1
Once we had finished simplifying the expressions, we found that two of the expressions simplified to the same thing, in this case 1. We used them to write the equation
1) Work with the more complicated side of the identity first
2) Rewrite both sides using sine and cosine
3) Use a Pythagorean identity
4) Simplify complex fractions or rewrite them
5) Use factoring (especially to create differences of squares)
A very important thing to remember when proving trigonometric identities is that you have to drop down "The Great Wall of China" and you can NOT cross it. This is because, when proving an equation, there is no way of knowing whether or not it is true.
So now that we have covered proving trigonometric identities, on to a new subject!!
EVEN AND ODD IDENTITIES!!
sin(-x)=-sinx cos(-x)=cos(x) tan(-x)=tan(x)
the sine and tangent functions and ODD functions
cosine is an EVEN function
ok so now i've gone through pretty much the entire class of today. There is only one more thing from class that i must remind you of:
sin(-x)=-sinx cos(-x)=cos(x) tan(-x)=tan(x)
the sine and tangent functions and ODD functions
cosine is an EVEN function
ok so now i've gone through pretty much the entire class of today. There is only one more thing from class that i must remind you of:
YOUR DANCING TOMMOROW!!!!
so i'd bring something comfy to wear. Mr.K said that as soon as you get into the room get into groups of four, with at least one person in your group that you have NEVER worked with.
One last thing. The scribe for tommorow is..... YI NAN!!!! =D
One last thing. The scribe for tommorow is..... YI NAN!!!! =D
Wednesday, March 11, 2009
BOB!!!!!!!!!!!!!!!!!!!!!!!!!!
Hey everyone. Well reflections is over. For me it seemed to be a really easy unit. The only problems that I have had at all so far is reading the question fully and properly :P, which has nothing to do with the unit. This unit was really easy to understand, once you remembered what A, B, C, and D are, how to find them, and what they do.
Just to recap on stuff that may have slipped your mind since we learned them:
1) A is how much a graph has been stretched. With trig functions it is the distance from the highest or lowest point on the graph to the sinusoidal axis.
2) B is NOT the period it is 2pi over the period
3) C is the distance along the x axis that the graph is shifting and is
4) D is the distance that the graph is shifted along the y axis
5) When dealing with B, factor it out of the bracket first
6) the inverse of a function of x is NOT the same as the resiprocal on a function of x
Well that's all for my BOB except for SLEEP, EAT, and BE ON TIME. lol bye
Just to recap on stuff that may have slipped your mind since we learned them:
1) A is how much a graph has been stretched. With trig functions it is the distance from the highest or lowest point on the graph to the sinusoidal axis.
2) B is NOT the period it is 2pi over the period
3) C is the distance along the x axis that the graph is shifting and is
4) D is the distance that the graph is shifted along the y axis
5) When dealing with B, factor it out of the bracket first
6) the inverse of a function of x is NOT the same as the resiprocal on a function of x
Well that's all for my BOB except for SLEEP, EAT, and BE ON TIME. lol bye
Wednesday, February 18, 2009
Circular Functions Reflection
Hey everybody. Since I know that if I leave this til later I'm gonna forget to do it, I will do it now just to be on the safe side. So, for me, circular functions was a pretty easy unit, and, although it was hard to remember all of the grade 11 work from last year after I had sat it at the back of my mind for months and months, it eventually became easy again. Here are a few things to remember that might catch you on the test if you don't:
1) you CAN NOT divide by a variable because, for all you know the variable could equal zero
ex. sinx^2=4sinx
sinx=4 WRONG
sinx^2=4sinx
sinx(sinx-4)=0
sinx=0, 4 RIGHT
In this case you would have been dividing by zero which would make the answer undefined
2) If you ever come up against a question where you are substituting a variable for a function times a variable, then the variable can not be the original variable from the equation. So if you get, for example, sinx in the original equation, the variable you substitute in for it CAN NOT BE X!!!!!!
3) remember that secant is 1 over cosine and cosecant is 1 over sine
4) If the denominator of anything is 0 than it is undefined. Remember that when your answering questions on the test, if the answer is undefined you have to state it with your answer.
Well that's about all I can think of at the moment. Good Luck to everyone on the test on Friday. Oh and remember the forgetting curve ( that sounds weird) and study what we've done this unit.
Bye =)
1) you CAN NOT divide by a variable because, for all you know the variable could equal zero
ex. sinx^2=4sinx
sinx=4 WRONG
sinx^2=4sinx
sinx(sinx-4)=0
sinx=0, 4 RIGHT
In this case you would have been dividing by zero which would make the answer undefined
2) If you ever come up against a question where you are substituting a variable for a function times a variable, then the variable can not be the original variable from the equation. So if you get, for example, sinx in the original equation, the variable you substitute in for it CAN NOT BE X!!!!!!
3) remember that secant is 1 over cosine and cosecant is 1 over sine
4) If the denominator of anything is 0 than it is undefined. Remember that when your answering questions on the test, if the answer is undefined you have to state it with your answer.
Well that's about all I can think of at the moment. Good Luck to everyone on the test on Friday. Oh and remember the forgetting curve ( that sounds weird) and study what we've done this unit.
Bye =)
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