I/D 1 unit N

1. Describe the 30* triangle : the 30 degree triangle has and angle of 30 degrees with a radiouse of 1
2. Describe the 45* triangle: this trangle has two of the same sides
3. Describe the 60* triangle: this triangle is like the opposite of the 30 degree triangle
4. How does this activity help you to derive the Unit Circle?this activities help me see the conection with in the unit cirlce and acutally understanding how they get each set of plots for each.
5. What quadrant does the triangle drawn in this activity lie in?  How do the values change if you draw the triangles in Quadrant II, III, or IV?  Re-draw the three triangles, but this time put one of the triangles in Quadrant II, one in Quadrant III, and one in Quadrant IV.  Label them as you did in the activity and describe the changes that occur.i kinda forgot because i dotn have the activity anymore
1. 1. The coolest thing I learned from this activity was that how the cricles are a bunch of trangles
   2. This activity will help me in this unit because it make me memorize more clearly how the circle works
   3. Something I never realized before about special right triangles and the unit circle is the they conect and that how easy it is

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.

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.