# Graphing Calculator Drawing: Rotation

*Absolute value graphs can be rotated to draw stars.*

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

** 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 $\theta$ about the origin by replacing $x$ and $y$ with the following expressions:

Note that $\theta$ should be given in radians, and one can convert degrees to radians by multiplying by the conversion factor $\frac{\pi}{180}.$

** 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 a chapter in the book Graphing Calculator Drawing Exercises.* *Suggested citation:* Skycak, J. (2019). Graphing Calculator Drawing: Rotation. *Graphing Calculator Drawing Exercises.* https://justinmath.com/graphing-calculator-drawing-rotation/