Trace the Sine Function

1 Explore

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.

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2 The Fine Print

**Requirements:**

These activities require web access using a browser that supports HTML5 and JavaScript. (That means almost any current browser.) No purchase is required, and there’s no advertising anywhere.

**Release Information**

Release: 2015Q4Update2, Semantic Version: 4.5.1-alpha, Build Number: 1026.6-wsp-widgets, Build Stamp: stek-macbook-pro/20180605163618

Web Sketchpad Copyright © 2017 KCP Technologies, a McGraw-Hill Education Company.

“You may freely use Web Sketchpad in your own Web pages, provided you do so for non-commercial use only” [per kcpt.github.io].

“You may freely use Web Sketchpad in your own Web pages, provided you do so for non-commercial use only” [per kcpt.github.io].

License: Creative Commons CC-BY-NC-SA 4.0

**Update History:**

23 April 2018: Uploaded version 1 of this page.