- Brian Sterr
A: The Original Circle
Building from the homework we can get a circle starting from the bottom and moving clockwise by using:
So we can use the equations:
Click "Animate" to see the point trace out the path described around the circle.
B. Vertical Translation
If we want to translate the whole circle up unit, we can add 1 to : Check box B, then Animate.
C. Horizontal Translation by a Constant
If we want to translate the whole circle right units, for example, we can add to : Check box C, then Animate.
D. Horizontal Translation by a Variable
If we want to translate the whole circle right units, for example, we can add to : Check box D, then Animate.
- Now the graph is being moved by a variable amount. Our original circle is being translated horizontally, but at the same time, the point is moving around the circle. When , the point will have gone all the way around the circle, which will now be units to the right of where it started.
- Notice that is exactly the circumference of the circle.
- Click “Show Circumference” and reset the animation to see how the circumference ‘unrolls’ along the x-axis.
- Every time the wheel makes one full rotation, the distance it moves equals the circumference.