Tips & Hints

Transformations
How I usually get through transformations is to remember what the original graph looks like.

For example,
f(x)=1+2cos(x)

The original equation is f(x)=cos(x).
Since f(x)= cos(x) looks like this:












I can assume that the entire graph moves up by one and the upper loop heightens by one and the lower loop lowers by one. Making the graph look like this:












Trigonometry
Probably the best tip is to just memorize all those flash cards. Yet, looking at the book for some guidance sometimes help. *Note: The book knows all.*

For the csc and sec are easy to remember. Sec sort of looks like cos but reverse so sec=1/cos. Csc is the only 1 that has a 's' in the middle of the 2 letters so I can say that 's' is the same for sin so csc=1/sin. Cot is the only 1 that has a 't' so cot=1/tan. Remembering the graphs are some what harder to remember. Just remember that "csc is next to y and pi and sec is the 1 on them." Since we know the graphs are just a bunch of parabolas, 'csc is next to y and pi' means that the parabola is next to these two attributes and it cannot land on y or pi. So what is between y and pi?Its π/2. Therefore, the vertex of the parabolas will be on every xπ/2 where x represents any number that is not divisible by 2. So π/2, jot down a dot, 3π/2 jot down another dot, -π/2, jot a dot, -π/2 jot another dot. To remember which parabolas goes upward and others go downward, just remember DUD or down up down (this also applies to sec). Meaning that the first parabola from your left will point downward, the 2nd will point upward and the third parabola will point downward. This ONLY applys to when your graph scale goes up to 2π. 'sec is the 1 on them' means that the vertex of the parabolas will touch the y-axis and every whole pi. That '1' represents that every vertex from both csc and sec will be 1 unit away from the x-axis. So at (0,1) jot down a dot, (π,1) jot down another dot and so on.

Probably the most worrisome thing from trigonometry for me would be using the unit circle for solving problems like (4,13) Find sinΘ or Find arctan(1).