I/D #1: Unit:N Special Right Triangles and the Unit Circle. How do they relate?

Inquiry Activity Summary

To derive the unit circle values, in class we would use visuals to help us remember. We used the Special Right Triangles to find the dimensions of the UC.

We First have to label the triangle according to the rules of SRT. We will use the 30 degrees triangle for this example. Since we are using a unit circle we know that the radius is one. so we have to divide it by 2X to make it one. And what you do to one, you do to the others. then you just use algebra to solve it. Once you have the X and Y you plot it at the top right corner.

 The 30 degrees triangle has angles 30,60,90 and the sides are r=1, x=radical3/2, y=1/2.

 The 45 degree triangle has the angles of 45,45,90. The sides are r=1, x=radical2/2, y=radical2/2

The 60 degree triangle has the angles 60,30,90. the sides are r=1, x=1/2, y=radical3/2. The 60 is the same as the thirty but just switched t the Y and X.

The points the top right corner that you write are the points on the circle that fits the degrees. Each of these triangles lie in the 1st. quadrant.

You can use the SRT concept for every quadrant but you have to change the sign in either the X or Y or both depending on which quadrant you want it in.

“The coolest thing I learned from this activity was if you can't memorize the unit circle, you can just use the SRT to get the answers.”

“This activity will help me in this unit because it will make it easier to complete the unit circle.”

“Something I never realized before about special right triangles and the unit circle is how they really do relate to one another and if you cant remember one, use the other for help.”