Graphing Calculator Drawing: Shading with Sine
High-frequency sine waves can be used to draw shaded regions.
This post is part of the book Graphing Calculator Drawing Exercises. Suggested citation: Skycak, J. (2019). Graphing Calculator Drawing: Shading with Sine. In Graphing Calculator Drawing Exercises. https://justinmath.com/graphing-calculator-drawing-shading-with-sine/
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Setup. Navigate to https://www.desmos.com/calculator. Be sure to sign in so that you can save your graph.
Demonstration - High Frequency. Observe the graph as you type each of the following inputs. In general, the graph of y=sin(vx) looks more and more solid as v increases.
Demonstration - Thickening a Curve. Observe the graph as you type each of the following inputs. In general, for large v, the graph of y=f(x)+Asin(vx) thickens the curve y=f(x) to have a vertical thickness of 2A.
Demonstration - Varying Amplitude. Observe the graph as you type each of the following inputs. In general, when v is large, the graph of y=f(x)sin(vx) shades the area between the graphs of y=−f(x) and y=f(x).
Demonstration - Shifts. Observe the graph as you type each of the following inputs. In general, the graph of y=f(x−a)sin(vx)+b is the graph of y=f(x)sin(vx) shifted right by a units and up by b units.
Demonstration - Limitations. Observe the graph as you type each of the following inputs.
Exercise. Reproduce the downward parabola shown below.

Exercise. Use the parabola as the amplitude of a high-frequency sine function to create a shaded area.

Exercise. Shift the shaded area up and right.

Exercise. Draw parabolas around the shaded area to create an eye.

Exercise. Create another eye.

Exercise. Create a parabola in the shape of a mouth.

Exercise. Thicken the parabola that forms the shape of the mouth.

Challenge. Make other kinds of emoji faces, such as a sad face or a laughing face.
This post is part of the book Graphing Calculator Drawing Exercises. Suggested citation: Skycak, J. (2019). Graphing Calculator Drawing: Shading with Sine. In Graphing Calculator Drawing Exercises. https://justinmath.com/graphing-calculator-drawing-shading-with-sine/
Want to get notified about new posts? Join the mailing list and follow on X/Twitter.