INQUIRY ACTIVITY SUMMARY
1. 30º Triangle:
The activity that we did during class shows us how this 30 degree triangle relates to the unit circle. Since this is a special right triangle, we have to label it according to the rules of Special Right Triangles. The hypotenuse is 2x, the horizontal value is x radical 3 and the vertical value is x. The hypotenuse must equal 1, so we need to divide it by 2x. This is done to all the sides. Then, the hypotenuse must be labeled r, the horizontal value x, and the vertical value y. Then, you need to draw a coordinate plane and finally find the ordered pairs. The ordered pairs are found by simplifying what you divided by 2x and then by thinking of this as a graph. The ordered pairs are (0,0) , (radical 3/2,0), and (radical 3/2, 1/2) (as shown in the picture above)
2. 45º Triangle
For the 45 degree triangle,we must first find the rules for special right tringles and label it according to that. The hypotenuse is x radical 2, the horizontal value is x, and the vertical value is also x. Everything must then be divided by x radical 2 because it was divided so that it would equal 1. When it is simplified, you will get 1/ radical 2, but you must remember to rationalize it because there cannot be a radical on the bottom of a fraction. The rationalized answer will be radical 2/2. Then, you must label the sides r, x, and y, the same was that the previous example was labeled. After, draw a coordinate plane and imagine it as if it were a graph. This is how you will get your points. The points will be (0,0), (radical2/2,0), and (radical 2/2, radical 2/2), as shown in the picture above.
3. 60º Triangle
The 60 degree triangle has the same rules that a 30 degree triangle has. So, the work is practically done for this. The only thing is to switch the x and y values. The ordered pairs would then be (0,0), (1/2,0), and (1/2,radical 3/2), as shown in the picture above.
4.This activity helps us derive the unit circle because we now know where the ordered pairs came from in the unit circle. The ordered pairs are achieved when you divide what you divided to get the hypotenuse to equal 1 (explained above) Also, When the coordinate plane is drawn, we can see that it is separated into the four quadrants that the unit circle has.
5. The trianges drawn all lie on the first quadrant. The triangles are simply reflected into all of the other quadrants and the x or y values change, depending on the quadrant.
30º Triangle:
The 30 degree triangle is reflected into all of the other quadrants. The x value becomes negative in the second quadrant. Both x and y values become negative in the third quadrant. The y value becomes negative in the fourth quadrant, as shown in the picture below. (changes are highlighted)
45º Triangle
The 45 degree triangle is reflected on all of the quadrants. The x value becomes negative in the first quadrant. The x and y values become negative in the third quadrant. The y value becomes negative in the fourth quadrant. (refer to picture below)
60º Triangle
The 60 degree triangle is reflected on all of the quadrants. The x value becomes negative in the first quadrant. The x and y values become negative in the third quadrant. The y value becomes negative in the fourth quadrant. (refer to picture below)
INQUIRY ACTIVITY REFLECTION
1. ''The coolest thing I learned from this activity was'' that the unit circle consists of special right triangles that make you not have to memorize the whole unit circle because of the patterns that it has. There is a meaning to the unit circle; it is not simply just a bunch of numbers.
2. "This activity will help me in this unit because" it will help me fill out the unit circle a lot faster and it will most likely increase my chances of filling out the unit circle accurately.
3. "Something I never realized before about special right triangles and the unit circle is" that by just knowing the first quadrant, you can fill out the others as well.
