Tips and Hints (my version anyway...)

Eh, I wasn't so fond of last week's post, and this one isn't all that much better...Enough of my useless ranting.

1.How do I remember transformations? First I start with the input (anything regarding the x). If the x is multiplied by something, I take the advice of a murderer who once said "Whatever your mind tells you to do, I implore you to do the opposite" (yes, bizare to take the advice of a murderer, but it works in this case). For example, when I see something like f(2x), i normally want to stretch the graph, but I do the opposite and compress ("shrink") it. If I see it has something added to it, like f(x+2), i want to shift the graph 2 units to the positive side (to the right), but instead I shift towards the negative side (to the left). In the case of subtraction, vice versa. If I see the output is multiplied by something, like 2 sin x, I just stretch it vertically according to the number (if the number is less than 1, compress it according to the number). When adding or subtracting to the output, add means up, subtraction means down. In short, for me, the trick is when changing the input, do the opposite of what you initially think and when changing the output, listen to your initial thoughts.

2.Trigonometry is simpler. When asked to find anything about the unit circle (coordinates, sin or cos of an angle, etc.), I just visualize how the triangle looks like in the unit circle and determine the needed information from that: the short side is 1/2 and long side is root of 3/2 for angle multiples of 30 degrees and all sides are root of 2/2 for multiples of 45 degrees (no, I don't actually have all the values memorized and can recall them in a second, I need the triangle for that). For graphs... I know how the curves for sin and cos look. All I need to know is where the hit the y-axis: if it's the origin, it's sin; if it's (0,1) it's cos. At that point, I just continue the curve. Tan, cot, csc, and sec , I don't have a trick, I just know those for some reason. Inverse graphs....those I actually need to memorize better before I get a trick to them (video games or memorizing the flash cards? damn procrastination...)

3. What worries me? Inverse graphs. I haven't memorized them and I need to know them (and the domain and range, now that I think about it...). Oh joy, more memorizing...

Note: Yes, it seems like they actually aren't tricks and I just memorized everything without tricks, but they are "tricks" to me.