Reflection #1- Unit Q :Verifying Trig Identities

1. To verify an Identity is to find what is giving using your rules or functions. You need to find each one by rules of other trigs to ether simplify them the most you can or in an equation to prove it out. There are many ways you can solve for a trig function. Not all the steps are right so  you can have your own way of doing it.

2.some tricks that i have are not really help full to most people but it helps me. I always look for anything that can be substituted.I look at old examples to see the procces and then i apply it. I also like to make the problem as simple as possible so that it wont confuse me.

3. These equations can be solved in so many ways. The steps i use in solving the equation start out with me looking at it and seeing if i can simplify it. the i look at each of the trigs and see if they are the same or not. After i look at that i see if any of them can be substituted to make them all match. After i do all that i just go with the flow and solve them by step by step. at the end i make sure my work is correct then move to the next problem.

SP7: unit Q concept 2 identities

 Please see my SP7, made in collaboration with Edna , by visiting their blog here.  Also be sure to check out the other awesome posts on their blog

I/D3: unit Q concept 1: Pythagorean Identities

Inquiry activity summery

 Where does sin^2x+cos^2x=1 ?
it comes form the Pythagorean theorem.  and the Pythagorean theorem is an identity its self.

What is the Pythagorean theorem using x,y and r?
the equation is A^2+B^2=C^2. when we plot the coordinate plane using the unit circle we get X^2+Y^2=R^2. x is the horizontal leg y the vertical leg and r the hypotenuse. and r being the hypotenuse make the equation equal to 1.

Pythagorean theorem equals to 1
as you can see this is just the Pythagorean theorem when you divide the R and it shows how cos and sin are in the equation. x/r being cos and y/r being sin. we when can consider it an identity.

showing that the identity is true.

drive the identity with secant and tangent
to find it we divide the equation by cos^2x
and as you simplify the equation it turn out

drive the identity with cosecant and cotangent
to find this we divided the equation by sin^2x
and like the top equation we simplify and we find it.

inquiry activity reflection
1. i have realize that in the few unites we have learned that all interconnect with each other.
2. if i had to describe trigonometry in three words i would describe them as interesting, hard, and fun.
i really like this unit and how it all connects. it makes you think and use the other chapters to think about it and.

Wpp13-14:concepts6-7 applications law of sines and cosine

Please see my WPP13-14, made in collaboration with edna , by visiting their blog here.here  Also be sure to check out the other awesome posts on their blog

BQ 1 Unit P

1. Law of sines: Why do we need it? How is is derived from what we already know?

https://www.youtube.com/watch?v=gAX_IleqeJQ



the height of the triangle gives us the right triangles we need to prove this. we use the reference angle using sin which is opposite over hypotenuse.






4. Area of formulas: how is the "area of an oblique" triangle derived? how does it relate to the area formula that you are familiar with?

http://www.ehow.com/video_12214809_area-oblique-triangle.html


an oblique triangle is a triangle that has no right triangle in it. the area of a triangle is base time height divided by 2. if you have a base and angle and a side you have enough to find the area.

Siting . https://www.youtube.com/watch?v=gAX_IleqeJQ
http://www.ehow.com/video_12214809_area-oblique-triangle.html

I/D 2 : Unit O Concept 7-8

This is the 30-60-90 triangle. As you can see i have drawn out the triangle and cut it in half making it a 30-60-90 triangle. each side of the triangle is 1 but after cutting it side c stays the same side a is 1/2 and side b is unknown. That's what we are trying to find. So we will use the Pythagorean theorem so solve for the side b. as seen in my work b is radical 3/2. 

This is a 45-45-90 triangle. As you can see i cut a square in half diagonally. Doing this i made the spacial right triangle. A all of the sides of the square are 1 so cutting it in 2 changes it. Side A and side B  are both equal to 1. angle C is the unknown one so that what we will be looking for using the Pythagorean theorem . In my work after i solved for C it is radical 2.

The N in front of each number like in the 30-60-90 triangle is just a variable in front of each side length  so show that all it is is a ratio. so that it doesn't really matter how big or small it is as long as it follows the ratio it is one of the two special right triangle.



Being able to derive these patterns myself aids in my learning because it shows me how each ratio was originally derived from and that it make me memorize the concept more.

RWA #1 Unit M Concept 5 elipses

RWA #1 Unit M Concept 5 elipses

1. Ellipse - The set of all points such that the sum of the distance from two points is a constant. 

The ellipse 

f

http://www.sparknotes.com/testprep/books/sat2/math2c/chapter8section4.rhtml

2.  To find the ellipse it has to be in standard conic form which is (x-h)^2/a^2+ (y-k)^2/b^2 = 1. It doesn't matter in what order a^2 and b^2 are they can be under whichever equation. h and k have to be in a specific one. H always has to be with x and k always has to be with y. another thing is that to determine the size of the ellipse if it's skinny or fat has to be based on x or y. If there ia a bigger number under x then it's fat, but if it's under the y then it's skinny. As you can see on the picture whatever d and d 2 are when they are added they equal 2a. 
    When graphed h,k will be center points. What ever numbers are on the bottom like we said then it  place will be a and the second one b.vertices come from a, co-vertices from b, and foci from c and we find c from a^2-b^2=c^2. If a has bigger numbers then it's our major axis and b will be minor axis. The foci will be on the major axis but a little before the vertices points. To determine the eccentricity of an ellipse,is e = c/a. So it's whatever number is c comes out to be divided by whatever number a is. 

http://www.youtube.com/watch?v=-OPR7Krjj7c

3.A great example for and an ellipse would be a chain on a bicycle. As your feet move on the handle . The hardest part or the part where its the  is the parking a lot.  and the chain is the circle that keep revolving 

4.

1  http://www.sparknotes.com/testprep/books/sat2/math2c/chapter8section4.rhtml
2  http://www.youtube.com/watch?v=-OPR7Krjj7c
3  http://mathforum.org/library/drmath/view/62576.html