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.