Student "edition" found at {csi dot journalspace dot com}.

Maybe I shouldn't have started this blog now, not with everything that's been going on.

I will continue with my discussion from yesterday of my second mechanics lecture class for the eighth week of the second term.

Basically, what the students have to determine, since most of the equations they have to work with are already given, is to list down the equations that include the quantity they are supposed to be looking for. This works with all problems already broken down to given and unknowns.

Then they also have to look at the given to see if there is any one equation where the unknown and all of the pertinent values are included. If so, it is just a matter of direct substitution to that equation.

If not, then they have to list down all the unknowns in equation with the least number of incidental unknowns. Then they look for any other equations not already listed that contain only that secondary unknown and the rest of the given values.

And so on. It either becomes a series of equation substitutions, or ending up with a system of n unknowns in n variables, which they should already be familiar with how to solve.

But back to the question we were working on in class. The problem with the variable we were looking for was that it was used in two different trigonometric functions in the final equation. So I had them recall our topic on trigonometric identities, and I was surprised at who was able to get the correct equation to use.

Since it was the equation from the Pythagorean relationship we used, there was a radical sign involved, which they also had to remove by squaring both sides of the problem, and so they ended up with an equation of degree four.

So an intermediate variable had to be used, whose degree one is equal to degree two of the original expression. Thus the working equation was reduced to a quadratic form, which could then be solved through the quadratic formula.

The result of the quadratic computation thus had to square rooted – if there is such a term – I’m not a grammar teacher after all, or as they are called locally, an English teacher. It doesn’t end there. Next, the inverse cosine of the value had to be obtained.

They ended up with two possible angles. That was the last part of the lesson: that given a point in two dimensional space that there would always be two angles that would pass through that point in the trajectory. Unless otherwise specified by the problem, both angles are correct.

Session 845 cannot be substituted in any of the given equations. Class dismissed.