In this activity, you can use the Animate tool to create and then animate a variable point along the orange domain segment. Label this point `x`, and then use the Measure Abscissa tool to measure its x-value.
You can then rotate the unit point—the point at `(1, 0)`—about the origin by an angle equal to your measured `x_x` in radians. Label this rotated point `P.`
✏️ How does point `P` behave when you drag or animate `x` along its domain?
✏️ If you make a graph of the height of `P` as a function of `x`, what will the graph look like? Draw a picture to show your guess about the shape of the graph.
Measure the height of `P` using the Measure Ordinate tool, and then plot the height `y_P` as a function of the `x`-value `x_x` of your animated point. Use one of the Trace tools to trace this plotted point, and then animate point `x` to trace out the graph. How well does it match your guess?
Your traced graph shows how `P` moves up and down as you animate `x`. But `P` also moves left and right.
✏️ If you make a graph of `x_P` as a function of `x_x`, what would the graph look like? Draw a picture to show your guess about the shape of this graph.
Use the Measure Abscissa tool to measure `x_P`, plot this new value as a function of `x_x`, and trace the result using a different color. Then animate to see what the new graph looks like.
2 The Fine Print