Transformations
The way i remember transformations is that they are counter intuitive. Usually the negative sign would mean shift x numbers of units to the left, but when it is in parenthesis, it means that u have to move it to the right. It usually means the opposite of what you think is right. When it is not in parenthesis, negative means down and positive means up.
ex. f(x-4) would mean that you have to shift the graph 4 units to the right.
ex. f(x)-4 would mean that you have to shift the graph 4 units down.
Trigonometry
The way I see trigonometry is by using my unit circle. I have memorized the unit circle from left to right and up to down. I know it pretty well now, it's just that when i have to draw it under pressure, i overthink things. =[
Well, the way i remember, it is that i remember the first quadrants, then i just mirror it from right to left, left to down, then left to right. The radians mirror, so it is, pi,pi/6,pi/4,pi/3,pi/2... from there it is mirrored. The first quadrant is positive, the second is negative positive, the third is all negative, and the fourth is positive negative. The quadrants are pretty easy, but the coordinates are a bit hard. It is kind of the same thing just different numbers, the zeros are pretty easy, its (1,0), (0,1), (-1,0), and (0,-1). The other coordinates are: (root of 3/2, 1/2), (root of 2/root of 2), then it is (1/2, root of 3/2). Then it is mirrored the same way.
What worries me?
Well, I need help on how to graph sin and cosine. I need to study the graphs more because I struggle through them. I also need help on finding the zeros of a graph. Any hints and tips would help me out... =]
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yEAH thats true when a number is in the parenthesis its sign either + or - will mean the positive. I was confused with that at first.:-s
ReplyDeleteto find the zeros of a graph is not that complicated..
ReplyDeletelets say you were given the function f(x)=(1/x)+2. All you have to do is switch it to an equation, y=(1/x)+2.
When the graph touches the x-axis, then that is considered a zero. So you know the zero is going to be a coordinate with the y being 0.
1. Plug in the 0 0=(1/x)+2
Now you are just trying to get x by itself.
2. Subtract 2 from both sides (1/x)=-2
3. Cross multiply -2x=1
4. Divide by -2 x=-1/2 or -0.5
Your zero for y=(1/x)+2 is (-0.5,0)
=]
counter intuitive? haha, yeah the adding and subtracting x inside and outside the parenthesis really bugged me. my graph would come out wrong for the longest time. if you subract AFTER the x had been altered, it moves down. otherwise its a horizontal shift when its inside the parenthesis.
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