This is a problem posed by my pre-calc instructor. I feel like this is somehow rudimentary, but I can't find a solution. The problem goes as follows:
Two gears are connected such that rotation of the smaller wheel causes the larger wheel to rotate. Through how many degrees will the larger wheel rotate if the smaller wheel rotates through an angle of 60 degrees.
He does supply a small diagram of a small circle (circle A) with a radius of 2 inches next to a larger circle (B) with a radius of 5 inches.
So far I've worked out the circumferences of both circles, with circle A being approx. 12.6 inches and circle B being approx. 31.4 inches. I'm also able to find the arc length of the 60 degree angle on the smaller circle, since 60 degrees = pi/3 and the arc is s = radius x theta radians, so the arc of the angle on circle A is approx. 2.1 inches.
Ultimately I'm confused in my thinking, because it seems like it'd be a simple ratio problem like between two 60/90/30 triangles of varying size. Problem is, I can't verify that the 60 degree change in the rotation of circle A being equates to 60 degrees of change in circle B. If anyone out there can give me a hand, I'll be infinitely grateful.