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UCD Maths Support Centre

Construction of the Sine Function

This interactive GeoGebra worksheet allows you to see how the graph of y=sin(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 sin(θ) at any particular point is given by the length of the vertical red line segment inside the circle. When the line segment is above the horizontal diameter, sin(θ) is positive and when the line segment is below the horizontal diameter, sin(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.