Yes, that's correct!

In fact, with sine modelling, Taylor series beats this approach with lower error. But with this you get to choose your properties so you might get more useful model instead.

Say, if you want to conjoin two sine models got from Taylor series to have it on a full [0, 2pi], you will have derivative discontinuity - a bump - on the joint. But with this model you wouldn't since it's explicitly required to be the inverse number at 0 and at pi/2.