Pythagorean Trigonometric Identity
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
|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.|
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.