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

INQUIRY ACTIVITY SUMMARY
1. For a 30 degree special right triangle, the rule is

30°	60°	90°
n	n√3	2n

Therefore, when we simply the hypotenuse to "1," by dividing each value by 2n, we get: r = 1 (hypotenuse), x = √3/2 (horizontal), and y = 1/2 (vertical). The work for dividing is shown below.

After finding the values, we can plot the special triangle onto a coordinate plane. If this triangle is put in the first quadrant, its coordinates would be (0,0); (√3/2,1/2); (√3/2,0).

 
2. For a 45 degree special right triangle, the rule is

45°	45°	90°
n	n	n√2

When we simply the hypotenuse to "1," by dividing by n√2, we get: r = 1 (hypotenuse), x = √2/2 (horizontal), and y = √2/2 (vertical). The work for dividing is shown below.

After finding the values, we can plot the special triangle onto a coordinate plane. If this triangle is put in the first quadrant, its coordinates would be (0,0); (√2/2,√2/2); (√2/2,0).

3. For a 60 degree special right triangle, the rule is the same as a 30 degree special triangle:

30°	60°	90°
n	n√3	2n

So, when we simply the hypotenuse to "1," by dividing each value by 2n, we get: r = 1 (hypotenuse), x = 1/2 (horizontal), and y = √3/2 (vertical). This is very similar to the 30 degree triangle. The only difference is that the x and y values are switched. The work for dividing is shown below.

After finding the values, we can plot the special triangle onto a coordinate plane. If this triangle is put in the first quadrant, its coordinates would be (0,0); (1/2, √3/2); (1/2, 0).

4. This activity helped me derive the Unit Circle by showing me that the Unit Circle is just made up of special right triangles. The 30, 45, and 60 degree triangles have the same coordinates as the first quadrant of the Unit Circle. And, if we use the reference angles of these triangles, we can get the coordinates of the remaining points on the Unit Circle.

5. The triangle in this activity lies in the first quadrant.  However, in the second quadrant, the x values are negative. In the third quadrant, both the x and y values are negative. Finally, in the fourth quadrant, the y values are negative. The first image shows a 30 degree special triangle in Quadrant II, notice how the x value is negative. The second image portrays a 45 degree special triangle in Quadrant III, notice how both the x and y value of the coordinates are negative. Finally, the third picture displays a 60 degree special triangle in Quadrant IV, notice how the y value is negative.

INQUIRY ACTIVITY REFLECTION
1. "The coolest thing I learned from this activity was:" that the triangles are in all the quadrants. They are just flipped around, so the coordinate signs change.
2. "This activity will help me in this unit because:" it helped me memorize the unit circle
3. "Something I never realized before about special right triangles and the unit circle is:" that the unit circle is completely made up of special triangles.