I/D #1: Unit N Concept 7: How do SRTs and UCs relate?

Inquiry Activity Summary:

1. The 30*  triangle has sides labeled (r,x,y). "r" stands for the hypotenuse; "x" adjacent or horizontal value; and "y" opposite or vertical value. After labeling the triangle according to the rules of Special Right Triangles, (r equals 1 from 2x/2x. y equals 1/2 from x/2x. x equals rad3/2 from rad3*x/2x.) Take note that the three sides are simplified so that the hypotenuse equals 1 (the radius of the Unit Circle is always equal to 1). Then, the hypotenuse was labeled with "r", the adjacent side with "x" and the opposite with "y". Next, I drew a coordinate plane, origin being located at the labeled 30 degrees (0,0) (so the triangle could lie in quadrant 1). and all three vertices labeled as ordered pairs: 60*  (1/2, rad3/2) and the last vertice 90* as (rad3/2,0) .


 













2. The 45* triangle was labeled according to the rules of SRT, taking note that each value was divided by rad2 so that the hypotenuse equals 1 (the radius of the Unit Circle is always equal to 1) (longest side, r, stood for rad2/rad2 equal to 1, 1/rad2 equal to rad2/2 and 1/rad2 equal to rad2/2). I labeled the hypotenuse "r", horizontal value "x", and vertical value "y". Next, I drew the coordinate plane labeling x and y axis and the origin of (0,0)  at the labeled 45*, the next point at (rad2/2, rad2/2) and the last at (rad2/2, 0). 




 3. The 60* triangle was labeled according to the rules of SRT dividing each side by 2x so that the hypotenuse equals 1 (the radius of the Unit Circle is always equal to 1), ("r" equal to 1 from 2x/2x; "y" equal to rad3/2 from xrad3/2x; "x" equal to 1/2 from x/2x). Next, I labeled the hypotenuse "r", horizontal value "x" and the vertical value "y". Lastly, I drew the coordinate plane labeling the x and y axis, origin at (0,0) and the corresponding ordered pairs per vertice (at 30*: (1/2,rad3/2) and (1/2,0) at 90*. 

 












4. This activity helped me derive the Unit Circle because it allows you to visually take note of where the angles and ordered pairs from the UC come to be and how each are solved for.  For example, taking a closer look at the 45* triangle, we could note where its ordered pair came simplifying each side using the rules of SRT. 

 (http://jwilson.coe.uga.edu/EMAT6680Su12/Jackson/Writeup10DMJ/Unit%20Circle.PNG)

5.  The quadrant drawn in this activity lies in the first quadrant (note all four quadrants in Figure 2). If you draw the 30* triangle in quadrant 2 it's csc/sin are positive, sec/cos and tan/cot negative are negative. In the third quadrant, tan/cot are positive, and csc/sin, cos/sec are negative. Lastly, note that cos/sec are positive and csc/sin, tan/cot are negative.

 (http://www.google.com/imgres?client=firefox-beta&hs=hI5&sa=X&rls=org.mozilla%3Aen-US%3Aofficial&channel=sb&biw=1280&bih=673&tbm=isch&tbnid=1aKd0mo1Wb16-M%3A&imgrefurl=http%3A%2F%2Fwww.sparknotes.com%2Fmath%2Ftrigonometry%2Ftrigonometricfunctions%2Fsection3.rhtml&docid=3IGWql635sbzWM&imgurl=http%3A%2F%2Fimg.sparknotes.com%2Ffigures%2F0%2F067486b8a9659518b7099dac07405d29%2Fquadrantsigns.gif&w=210&h=210&ei=UlUJU5DHF7LlygGK8YGQDw&zoom=1&ved=0CFcQhBwwAQ&iact=rc&dur=442&page=1&start=0&ndsp=17) 

 

(https://encrypted-tbn0.gstatic.c/images?q=tbn:ANd9GcTokzujb26VtG3kOJjr5Hiq9rR1O7TWjkroQ8gv_peFYJc6oBNBUA)

Inquiry Reflection Activity: 

1. The coolest thing I learned from this activity was learning a basis for trigonometry using the rules for SRTs and UCs! Seeing how the curriculum for geometry and trigonometry tie together is fascinating!
2. This activity will help me in this unit because finding the value for the trig functions are more easily solved if you understand the unit circle in more depth. 
3. Something I never realized before about special right triangles and the unit circle is how they related with each other and the components that are used carefully to calculate each angle and degree that make up the unit circle.

References:

• http://jwilson.coe.uga.edu/EMAT6680Su12/Jackson/Writeup10DMJ/Unit%20Circle.PNG
• https://encrypted-tbn0.gstatic./images?q=tbn:ANd9GcTokzujb26VtG3kOJjr5Hiq9rR1O7TWjkroQ8gv_peFYJc6oBNBUA
• http://www.google.com/imgres?client=firefox-beta&hs=hI5&sa=X&rls=org.mozilla%3Aen-US%3Aofficial&channel=sb&biw=1280&bih=673&tbm=isch&tbnid=1aKd0mo1Wb16-M%3A&imgrefurl=http%3A%2F%2Fwww.sparknotes.com%2Fmath%2Ftrigonometry%2Ftrigonometricfunctions%2Fsection3.rhtml&docid=3IGWql635sbzWM&imgurl=http%3A%2F%2Fimg.sparknotes.com%2Ffigures%2F0%2F067486b8a9659518b7099dac07405d29%2Fquadrantsigns.gif&w=210&h=210&ei=UlUJU5DHF7LlygGK8YGQDw&zoom=1&ved=0CFcQhBwwAQ&iact=rc&dur=442&page=1&start=0&ndsp=17 
• http://dj1hlxw0wr920.cloudfront.net/userfiles/wyzfiles/8c85deff-b9ed-4c80-8b44-16e8e9322af2.png
• https://encrypted-tbn0.gstatic.c/images?q=tbn:ANd9GcTokzujb26VtG3kOJjr5Hiq9rR1O7TWjkroQ8gv_peFYJc6oBNBUA