Tips and Hints

I feel like I'm posting false information... Such a high self esteem huh? Anyways, I can't explain really well so don't take my word for it. Really... >___>;;

1. Transformations. Makes graphing an equation much easier if you know how. Easy on some parts, somewhat confusing on the rest. The key to graphing any function or equation is knowing your parent functions.

Equations like f(x)=(x-2)-3 is easy; shift the graph over 2 units to the right on the x-axis, and then sift it 3 units down on the y-axis. But, what if we are to transform functions based off the unit circle like sin(x), cos(x), and tan(x)?

Let's use sine for our formula example:

f(x) = asinb(x-c)+d

• a would tell us how 'tall' or 'short' the graph will be. In other words, it tells us our amplitude.
  
• b makes the function either thinner or wider, thus causing our period to change. To find out our period, we use 2π/b. If a>1, the thinner it is, if a<1>
• c moves the graph along the x-axis. But it gets tricky when changing the input because then you'd have to do the opposite. But this formula actually clarifies which direction to go. If you plug in a negative number for c, you'd get a positive, and if you plug in a positive number you would get a negative.
• d shifts the graph along the y-axis, no confusion there. :]
  

2. Trigonometry. I think of the unit circle, triangles, sine, cosine, tangent and whatnot. What I remember most is SOH CAH TOA. (.___. ;;) Finding the radians and degrees are becoming clearer in a way but I have no advice for that. I remember what Ms.Gapac told us to help us find the positive values; All Students Take Calculus. That goes in the quadrant order, which means in the first quadrant, All (sine, cosine, and tangent) are positive. Sine is positive in the second quadrant, Tangent is positive in the third, and Cosine is positive in the fourth. The reciprocal of a trig function is not the same as the inverse! Eh, not much really to remember right now...

3. What confuses me? What worries me?? MANY MANY THINGS. But trigonometry wise, I can't be confused if I don't know anything :D
lol, I still get confused with remembering how the inverses look like and such. Domain and ranges are a pain to remember too. But we haven't really gotten deep into trig yet so i must wait and see what i must worry about later on. But none the less, I hope that there would be some good advice on trig, it would make it alot easier. :3


Happy Saturday...no wait, Sunday!!!