Tips and Hints

1. Share how you remember Transformations. Do you have any tips or hints that help you remember?
   

Flips, Slides, Stretches and Squishes!!

SLIDES:

When starting with the function of f(x) focus on where the points will go then focus on the the graph is going to look like. When something is added or subtracted from a function then the function shifts the graph vertically. Lets say you add 3 to the function of "P" then this indicates that P will move 3 times up and if you subtract 4 then the graph will move vertically 4 units down. Therefore, the point on the graph of f(x)-3 should be plotted 3 units down the original graph of f(x)
Adding parentheses to a function determines the operation shifting horizontally on the graph. Subtracting moves the graph to the right and adding will shift the graph to the left. The graph of f(x-3) is the same as f(x) but the only difference is that it will move 3 units to the right. The parentheses with f(x-3) moves the function RIGHT not left but will adding then it moves LEFT not right. Merely think of this as the opposite...the opposite of right is left and left is right.
FLIPS:
Basically the graph of -f(x) is the reflection of f(x) across the x-axis. The trick here is to keep in mind a mirror image of the graph. How would it look like if you folded it, turned it, had it overlap and etc. Multiplying x by negative one has the graph reflect across the y-axis; if f(x) has the point (a,b) then f(-x) has the point (-a,b)
SQUISHES:
Multiplying the y-values by 1/2...affects the y values. If the graph of f(x) has the point (x,y) then the graph of f(x)timesE has the point (x,Etimesy) In this case each point on 1/2 f(x) is half of the distance from the x-axis as the point of the graph of f(x). When you have a number outside the parentheses such as 2f(x) then you are simplying making it smaller.
STRETCHES:
Multiplying f(x) by a number affects the distance of the points from the x-axis which leads to stretching it away from the x-axis. Multiplying x by a number inversely affects the distance of a function's coordinates from the y-axis. When you have a number inside with the x then you are stretching that out.

2. Share how you remember or understand trigonometry. Do you have any tips or hints that you remember/ memorize all those facts?

Unit Circle

Okay some of the tricks I learned by myself were the values of the unit circle. Think of 2pie as your starting point. since its on the right side of the unit circle and on the horizontal line then visualize it like a graph. On the right of the horizontal line you your positive numbers...well 2pie is point (1,0) because its on the right side of the graph on the horizontal line...Now the opposite of 2pie is pie which is on the left side of the graph, so e know that pie's point is (-1,0) because all numbers to the left of the horizontal line on a graph are negative. Now the vertical line as we know is y...and for the unit circle you can use it as so to assist you. The top of the unit circle is pie/2...think of this as whats half of pie...so the top has the points of (0,1) because its on y. The opposite of pie/2 is 3pie/2 which has the point (0,-1) Okay going back to 2pie, from that point going counter-clock wise we will hit pie/6, then pie/4 then pie/3 from this point on its an order...after pie/3 we come across pie/2 which is half of pie. okay since our last number was pie/3 then we will come across 2pie/3. Okay now the sequence i am trying to show you is: 6, 4, 3...3, 4, 6...6, 4, 3...3, 4, 6. This indicates that the unit circle is divided into four sections. think of the unit circle as a division of 4 quadrants. Okay know that you have those denominators its time to add the numerators. the right upper quadrant of the unit circle all consists of just pie on top of the denominator such as pie/6 and pie/4 and pie/3. The second quadrant which is the left upper one will be filled up as the following: the number over 3 will be 2. The next number over 4 will be 3pie/4 now the trick for these is that in Q1 you have pie/4. okay count this one as one and next count pie/2 as number two then in Q2 3pie/4 will be three hence "3"pie/4..then pie will be number 4...the in Q3 5pie/4 will be number five hence "5"pie/4 then 3pie/2 will be counted as number six and 7pie/4 will be number 7 because "7"pie/4....Now i rather explain the rest visually...MOVING ON
the values for the domains are quiet simply....anything with a denominator of four corresponds to the square root of 2/2
Anything with a denominator of 6 will be square root of 3/2, 1/2
Anything with the denominator of 3 will be 1/2 first THEN square root of 3/2

3. What still confuses you or worries you about trigonometry?
Well so far i understand everything...i know my unit circle even with the pressure of writing it in 2.5 time...I believe i know how to graph them...possibly the inverses of the functions along with the domain and the range...but i know i will learn that during the weekend because i have a a book that will help me.