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UCD Maths Support Centre

Construction of the Cosine Function

This interactive GeoGebra worksheet allows you to see how the graph of y=cos(θ) is constructed as a point moves around a unit circle. You can control the point by moving the slider. Have a go and see what happens!

The worksheet will also construct the graph automatically if you press the 'Animation on' button. To stop the animation, you should click on the icon that will appear at the bottom left of the screen.

The value of cos(θ) at any particular point is given by the length of the horizontal red line segment inside the circle. When the line segment is to the right of the centre of the circle, cos(θ) is positive and when the line segment is to the left of the centre of the circle, cos(θ) is negative.

If you want to return the slider to its original position, then simply click on the icon in the top right hand corner of the worksheet.