Graphing Calculator Drawing: Rotation
Absolute value graphs can be rotated to draw stars.
This post is part of the book Graphing Calculator Drawing Exercises. Suggested citation: Skycak, J. (2019). Graphing Calculator Drawing: Rotation. In Graphing Calculator Drawing Exercises. https://justinmath.com/graphing-calculator-drawing-rotation/
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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 - Rotation. Observe the graph as you type each of the following inputs. In general, a graph can be rotated by an angle of θ about the origin by replacing x and y with the following expressions:
Note that θ should be given in radians, and one can convert degrees to radians by multiplying by the conversion factor π180.
Exercise. Reproduce the graph below by drawing an absolute value function and then rotating it a fifth of a circle counterclockwise.

Exercise. Continue drawing rotated absolute value functions to form a star.

Exercise. Draw a circle that passes through the sharp points of the star.

Exercise. Add a background layer by drawing rotated parabolas.

Exercise. Finally, add non-Euclidean ellipses to the background.

Challenge. Create your own emblem.
This post is part of the book Graphing Calculator Drawing Exercises. Suggested citation: Skycak, J. (2019). Graphing Calculator Drawing: Rotation. In Graphing Calculator Drawing Exercises. https://justinmath.com/graphing-calculator-drawing-rotation/
Want to get notified about new posts? Join the mailing list and follow on X/Twitter.