Archive for October, 2024

Remembering Inverse, Converse, and Contrapositive of if-then Statements

If we have our statement p then q:

The inverse is inverting the signs think of i as the square root of -1. You are negating each element.

~p -> ~q

Converse, reverse.

q -> p.

Once you remember those, just remember that the contrapositive is converse and inverse combined.

~q -> ~p

Sine gets the mine, tADDngent, and se cant keep that constant. Remembering trigonometric substitutions.

In Calculus II we learn the wretched “Trigonometric substitution” and it can be hard to remember them. I came up with this little pneumonic device to help me out. Is it good? Not at all. Did it help? Yes, it did.

a^2-x^2 = sin^2x: Sine gets the mine.

a^2+x^2 = tan^2x: Remember the A in tAngent and the A in Add. Taddgent.

x^2-a^2 = sec^2x: She cant keep that constant = secant keep that constant.

These are stupid but I hope that they help.