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

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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 *alpha*between 0 and 360^{o}. 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 90^{o}. 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 90^{o}angle.

**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 On*button.

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