October 24, 2010

ICT in Maths, converting circular motion into trigonometric graphs (Geogebra)

Writing about web page /jbrookes/entry/ict_in_maths/

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I have created an improved geogebra file that uses an animated angle to plot the graphs of sin, cos and tan x.  trigtrace-simpler.ggb.  I have included instructions as to how it was created below.

Setting up the circle.

Create a circle centred at A=(0,0) passing through point B=(1,0). Then create a slider for an angle alphabetween 0 and 360o. Next create an angle with given size (Leg point B, vertex A, size alpha). This should put a point B’ on the circle which will move around as the slider is moved. Right click the slider and select Animation on: B’ should move around the circle.

Plotting sin x.

In the input box [at the bottom of the page] enter “C=(alpha,0)” [using the drop down menu to select alpha]. This should create a point on the x-axis that moves as the angle changes. Now create a vertical line through C [Line perpendicular to x-axis], and a horizontal line through B’ [Line perpendicular to y-axis]. The point at the intersection [Intersect two objects] will now trace out the graph of sin x.

Plotting cos x.

cos x = sin (x+90). Therefore, create an angle with leg-point B’, vertex A and given size 90o. This will be point B’’. A horizontal line through B’’ will meet the vertical line through C at a point, which will trace out cos x.

Plotting tan x

For this, we need a line through B’ and A, and another vertically tangeant to the circle at B. Where these two lines meet has y-value of tan(alpha), because the circle has radius 1. A horizontal line through this point will meet the vertical line through C, to trace out tan x.

Drawing the graphs

By selecting the trace on our three moving points we can see the graphs they produce. Alternatively, by entering y=sin(x), etc. into the input box we can display the graph.

Differences from original.

In the original file there is an extra vertical line through B’ and some segments that form a triangle inside the circle when all the Lines are hidden. Also, the right angle used in the cos x construction used a perpendicular line rather than a 90oangle.

Creating the slider/animation

The second to last icon allows a slider to be generated anywhere on the diagram. This is basically a variable which can be used to replace a number in a command. The context (right-click) menu then has an Animation Onbutton.

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