Learn how to visualize the Pythagorean Trigonometric Identity.

Step 1: Try out the GeoGebra applet

Drag the green point and explore how the position of the red point changes.

Step 2: Watch the tutorial video

Step 3: Create the construction yourself

Construction Steps

1.

Enter f(x) = sin(x)^2 in the input bar.

2.

Enter g(x) = cos(x)^2 in the input bar.

3.

Select the Point tool in order to create a point A on the x-axis.

4.

Enter a = x(A) in order to extract the x-coordinate of point A.

5.

Create a point S = (a, f(a) + g(a)), with the same x-coordinate as point A, but which shows the sum of the two functions f and g at this coordinate.

6.

Trace on Icon

Turn on the trace of point S by making a right click (MacOS: cmd-click) on the point and selecting Trace On in the appearing window.

Task

Select the Move tool and drag point A along the x-axis. As point S follows along, its trace visualizes the sum of the two functions sin²(x) and cos²(x). Make an assumption about which function could be used to describe the path of point S. Check your assumption by entering it in the Algebra View.