# Graphing Calculator Drawing: Shading with Sine

*High-frequency sine waves can be used to draw shaded regions.*

*This post is a chapter in the book Graphing Calculator Drawing Exercises.* *Suggested citation:* Skycak, J. (2019). Graphing Calculator Drawing: Shading with Sine. *Graphing Calculator Drawing Exercises.* https://justinmath.com/graphing-calculator-drawing-shading-with-sine/

** 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 $y=f(x)+A\sin(vx)$ 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 a chapter in the book Graphing Calculator Drawing Exercises.* *Suggested citation:* Skycak, J. (2019). Graphing Calculator Drawing: Shading with Sine. *Graphing Calculator Drawing Exercises.* https://justinmath.com/graphing-calculator-drawing-shading-with-sine/