I/D 1: Unit: N- How do SRT and UC relate?

A)

Here we are dealing with a 30* angle in which the horizontal side is x radical 3, the vertical side x, hypotenuse 2x. We start of by dividing everything by 2x because we need hypotenuse to be one. After canceling out the x we are left with a vertical side of 1/2, horizontal side of radical 3/2, and hypotenuse of one. Afterwards we plot it on the first quadrant deriving the ordered pairs of (radical 3/2,1/2), (radical 3/2,0), and (0,0) as the center. 

B) 

This triangle is a 45* angle and the labeling of the sides differs than those of the 30* angle. Here both the vertical and horizontal side are radical 2/2 and the hypotenuse is 1. We the just plot it on the first quadrant and get the ordered pairs of (0,0), (radical 2/2,0), (radical 2/2, radical 2/2). 

C) 

This is a 60* angle and it is similar to the 30* angle it's just that the sides are switched around. The hypotenuse still being 2x, the vertical side x radical 3, and the horizontal side as x. We first divide everything by 2x and we get a vertical side of radical 3/2, a horizontal side of 1/2, and hypotenuse of one. Next we place the triangle on the first quadrant giving us ordered pairs of (1/2, radical 3\2), (1/2,0), and (0,0). 

This activity helps me derive the unit circle by allowing me to know the ordered pair of a 30*, 45*, and a 60* angle. Which are the basic three triangle used in the entire unit circle. By drawing triangles on the first quadrant we get the positive ordered pairs. When triangles plotted on the 2nd quadrant ordered pairs would have a negative x value. When in the 3rd quadrant both x and y would have a negative values. When in the last quadrant (4) the y value will be negative. Other bottom image shows how the triangles are just flipped around depending on the quadrant it's in. 

 

1. THE COOLEST THING I LEARNED FROM THIS ACTIVITY WAS: that the unit circle primarily consists of these three triangles a 30*, 45*, and a 60*. That they only get flipped around depending on the quadrant they are in. 
2. THIS ACTIVITY WILL HELP ME IN THIS UNIT BECAUSE: it's another way to find the ordered pairs in the unit circle. So in case I forget one of them I can use this tool  to help me find the ordered pair. 
3. SOMETHING I NEVER REALIZED BEFORE ABOUT SPECIAL RIGHT TRIANGLES AND THE UNIT CIRCLE IS:  something that I had not realized about right triangles is that they played an important part I. The unit circle. And something that the unit cicle has is that it involves same points just switched around depending on the quadrant.