331: Which values of x do we choose? Trigonometry.

For the following functions, think about "How to graph like a math teacher." Math teachers want to sketch graphs quickly and efficiently and choose values of x that work "nicely" in the equation and  generate integer values of y, thus making it easier to graph.

• Which points are best found by inspection?
• Which points are best found by substitution?
• Which points are best found by symmetry?

$y = sin(3\theta)$

$y = \Big{sin(\theta)}^2$

$y = sin^{-1}(\theta)$

$r = 3sin(3\theta)$

What are your favorite examples of this?