You really don’t want to read all the details. But among the crucial steps in getting the lesson outlined last time to work right, the crucialest might be the place where the students figure out that the y-scale goes as the secant.
How do we help them figure that out? (And what do we mean by that?) That’s what we’ll talk about today.
First of all: that y-scale is the number of centimeters per degree in the y-direction, and that depends on latitude. And when you look at a Mercator-projected Earth (like the one in the figure) you can see that this scale increases with latitude. How do we know? Because the lines of latitude get farther apart. So more centimeters per degree.