Pythagorean Trigonometric Identity

[size=100]Learn how to visualize the Pythagorean Trigonometric Identity.[/size]
Step 1: Try out the GeoGebra applet
[size=100]Drag the green point and explore how the position of the red point changes.[/size]
Step 2: Watch the tutorial video

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Step 3: Create the construction yourself
Construction Steps
[size=100][table][tr][td]1.[/td][td][/td][td][size=100][size=100]Enter [i]f(x) = sin(x)^2[/i] in the input bar.[/size][/size][/td][/tr][tr][td]2.[/td][td][/td][td][size=100]Enter [i]g(x) = cos(x)^2[/i] in the input bar.[/size][/td][/tr][tr][td]3.[/td][td][icon]/images/ggb/toolbar/mode_point.png[/icon][/td][td][size=100]Select the [i]Point[/i] tool in order to create a point [i]A[/i] on the x-axis.[/size][/td][/tr][tr][td]4.[/td][td][/td][td][size=100]Enter [i]a = x(A)[/i] in order to extract the x-coordinate of point [i]A[/i].[/size][/td][/tr][tr][td]5.[/td][td][/td][td][size=100]Create a point [i]S = (a, f(a) + g(a))[/i], with the same x-coordinate as point [i]A[/i], but which shows the sum of the two functions [i]f[/i] and [i]g[/i] at this coordinate.[/size][/td][/tr][tr][td]6.[br][/td][td]Trace on Icon[br][/td][td][size=100][size=100]Turn on the trace of point [i]S [/i]by making a right click (MacOS: cmd-click) on the point and selecting [i]Trace On[/i] in the appearing window. [/size][/size][br][/td][/tr][/table][br][/size][br][size=100][br][/size]
[size=100]Select the [i]Mov[/i]e tool and drag point [i]A[/i] along the x-axis. As point [i]S[/i] follows along, its trace visualizes the sum of the two functions [i]sin²(x)[/i] and [i]cos²(x)[/i]. Make an assumption about which function could be used to describe the path of point [i]S[/i]. Check your assumption by entering it in the [i]Algebra View[/i].[/size]

Information: Pythagorean Trigonometric Identity