It's required to make a good grade as it is taught today, yes. That's because it's traditionally taught after trig so they just go ahead and integrate it, but there's no reason why you couldn't teach it before and then, during trig, throw in how to differentiate/integrate trig functions as well as the useful trig identities that show up in integrating certain functions.
Trust me as someone half-way through an engineering PhD, as I said before, the core concepts of calculus do not require trigonometry to be taught. Rate of change, cumulation (integration), and limits can all be taught without trig. Hell, you can teach them all with just polynomials.
If you don't understand that, perhaps it's because you couldn't see the forest for the trees. If you came away from calculus thinking that it is closely related to trig in a special way moreso than other math topics (like algebra, logarithms, exponents, etc.) then the education system has failed you.
Great explanation. Maybe more of a hybrid approach, where they teach principals side by side, that way you get a refresher each year (which most students need anyways after summer... or covid).
I do think you would miss out if you didnt understand polar coordinates during integration though.
It's required to make a good grade as it is taught today, yes. That's because it's traditionally taught after trig so they just go ahead and integrate it, but there's no reason why you couldn't teach it before and then, during trig, throw in how to differentiate/integrate trig functions as well as the useful trig identities that show up in integrating certain functions.
Trust me as someone half-way through an engineering PhD, as I said before, the core concepts of calculus do not require trigonometry to be taught. Rate of change, cumulation (integration), and limits can all be taught without trig. Hell, you can teach them all with just polynomials.
If you don't understand that, perhaps it's because you couldn't see the forest for the trees. If you came away from calculus thinking that it is closely related to trig in a special way moreso than other math topics (like algebra, logarithms, exponents, etc.) then the education system has failed you.
Great explanation. Maybe more of a hybrid approach, where they teach principals side by side, that way you get a refresher each year (which most students need anyways after summer... or covid).
I do think you would miss out if you didnt understand polar coordinates during integration though.