Graphing Calculator Drawing: Rotation

by Justin Skycak (@justinskycak) on

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:

xxcosθ+ysinθyycosθxsinθ


Note that θ should be given in radians, and one can convert degrees to radians by multiplying by the conversion factor π180.

ycosπ6xsinπ6=(xcosπ6+ysinπ6)2(xcosπ4+ysinπ44)2+(ycosπ4xsinπ42)2=1


Exercise. Reproduce the graph below by drawing an absolute value function and then rotating it a fifth of a circle counterclockwise.

image


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

image


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

image


Exercise. Add a background layer by drawing rotated parabolas.

image


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

image


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.