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

1. 30 Triangle 

The triangle is at quadrant one and label the three sides. Hypotenuse is 2x, adjacent is x radical 3, and opposite is x. To get the values we will need to derive them. For hypotenuse divide by 2x to get one (r value), for adjacent divide by 2x to get radical 3/2 (x value), for opposite divide by 2x to get 1/2 (y value). Finally draw the coordinate planes (0,0) as the orgin, (radical 3/2,0) as the x axis, (radical 3/2,1/2) as the y axis. 

30 triangle

2. 45 triangle

 The triangle is at quadrant one and label the three sides. Hypotenuse is x radical 2, adjacent is x, and opposite is x. Then derive to get the values. For hypotenuse(r) divide by x radical 2 to get one, for adjacent(x) divide by x radical 2 to get 1/radical 2 then rationalize to get radical 2/2, and for opposite(y) divide by x radical 2 to get  1/radical 2 then rationalize to get radical 2/2. Finally draw the coordinates planes, (0,0) as the origin, (radical 2/2) as both the y and x axis. 

45 triangle

3. 60 triangle 

The triangle is at quadrant one and label the three sides. Hypotenuse is 2x, adjacent is x, and opposite is x radical 3. Then derive to get the values. For hypotenuse(r) divide by 2x to get one, for adjacent(x) divide by 2x to get 1/2, and for opposite(y) divide by 2x to get radical 3/2. Finally draw the coordinate planes, (0,0) as the origin, (1/2,0) as the x axis, and (1/2,radical 3/2) as the y axis. 

60 triangle

How does this activity help you to derive the Unit Circle?

This activity helps me derive values that are in the unit circle. Also the values are either positive or negative depending on what quadrant it lies on. All the values and trig functions in quadrant one are positive, in quadrant two the x axis is negative and sine and cosecant are positive, in quadrant three both x and y axis are negative and tangent and cotangent are positive, and for quadrant four the y axis is negative.

THE COOLEST THING I LEARNED FROM THIS ACTIVITY WAS that the triangles and its coordinate planes make up the entire unit circle. Also when dividing with the value of hypotenuse on the adjacent and opposite sides gets us the values from the unit circle. 

THIS ACTIVITY WILL HELP ME IN THIS UNIT BECAUSE now I know what order pair goes in what degree all thanks to the 30, 45, 60 triangles. Also where the values and trig functions are positive or negative. 

SOMETHING I NEVER REALIZED BEFORE ABOUT SPECIAL RIGHT TRIANGLES AND THE UNIT CIRCLE IS that deriving the triangles to get the same values from the unit circle would be easy get. Also that the unit circle was made from the 30, 45, 60 triangles.