I’m not sure who came up with this — this simple diagram reflects all possible true trigonometric identities of the form *x* ÷ *y* = *z* or *x* × *y* = *z*, where *x*, *y*, and *z* are the basic trigonometric functions of the same angle *t*.

For any three neighboring functions on the perimeter of the star, the product of the ends always equals the middle (e.g., tan *t* × cos *t* = sin *t*) and the middle function divided by one of the end functions is equal to the other end function (e.g., sin *t* ÷ tan *t* = cos *t* and sin *t* ÷ cos *t* = tan *t*). If you memorize the diagram you can reel off a list of 18 simple relations.

I found it in Michael Stueben’s *Twenty Years Before the Blackboard*, 1998.