Mathematical functions can be some of the most interesting animations generated in Motion5. Mathematical functions can easily be created and animated in Motion5, using lines for graphs and bezier curves to represent sine and cosine waves.

Looking at the animation shown below, if you put the the angle measure θ on the horizontal axis of a standard graph in the x,y-plane and take the output (the value of sin(θ) = y) and use this value as the height of the function, the result looks like this:

To recreate the graph (X,Y coordinates) in this animation, use the Text and Line tools. Use the Shape tool, outline only, no fill, to recreate the circle. Use the Shape tool once more, bezier type with smooth control points at intersecting lines, to recreate the Sine Wave (blue). Add a Write On behavior to this line to demonstrate how the sine’s values repeat with every length of 2π, resulting in a curved wave.

Recreate the green line representing the angle by using the Shape Tool, and fix the anchor point at 0,0 coordinates in the circle graph. In the Inspector, keyframe this line on the rotational Z axis from 0 degrees to 360 degrees for a full circle. Recreate the red line representing the value of sin (θ) = y by using the Shape Tool and animate the line in the Inspector, using the position and crop parameters.

The next time you need to teach an equation, function or concept, consider using Motion5 to visually bring the content to life and improve your students’ conceptual understanding, fluency and application of your course material!

Written by Kate Lee, Smith College Senior Media Producer