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

No entry yesterday because I didn't go to school. Not because of the transport strike, although that played a part in hindering my plans to go back to school in the afternoon. In the morning I was out of town for a meeting in another school in the system.

Monday I started on the last topic for Trig, which is the Law of Sines and the Law of Cosines, applying the trigonometric functions for oblique triangles, or those without any right triangles.

I was able to derive the equations using the inherent right triangles in any olbique triangle, and although the students will remember easily the law of sines (which is basically "side a over sine of angle A equals side b over sine of angle B equals side c over angle C") there was a little difficuly in seeing the applicability of a "three-side" equation.

This became obvious when I had to list down when the law of sines may be used, which is either when two angles and the length of one side are given, or when two sides and the length of one opposite side is given.
I checked the given quantities and asked them if all the other unknowns were solvable. There were times when even though only one quantity from each of the three "sides" of the equation was given, that there were still students who said, "Yes."

Maybe they weren't really paying attention. Maybe it's one of the natural consequences of having an early morning class. Either way I had to write out when exactly they were supposed to use the law of sines, and when they were to use the law of cosines.

The law of cosines could be used when they are given either the lengths of the three sides or the lengths of two sides and the value of the angle between them.

In my mechanics classes we talked about two dimensional collisions, and I gave them the equations for when linear momentum is conserved and when mechanical energy is conserved in those situations.

Since these are two equations that use the two masses and the four velocities of the masses involved in the collision, both before and after, from there we were able to derive the equations for the two final velocities using only the two masses and the two initial velocities.

We also had to give the equations for getting the x and y components of the four velocities given the magnitudes and the angles, again using the same sine and cosine equations we used in two-dimensional motion. That was the first step in solving for two-dimensional collisions.

The next step is using one equation of conservation for the x axis, and another one for the y axis. Then, if the resultant velocity is required, they could get it using the pythagorean formula, and the angle using the arctangent.

What was tiring was writing those for equations four times, two for the initial velocities of mass one and two, and two for the final velocities of mass one and two. It was only after they were all spelled out that the students realized what I meant by using those equations in four situations.

I was probably very close to being asked to write down the four equations of conservation along the x and the y axes, but maybe they already saw what I meant from the repeated formulas.

Hopefully next time I'll just have visual aids for those formulas.