Is there an easy way to remember the special 8 trig. identities

In my AP Pre-Calc 2 class, we were given a list of trig identities to memorize.

i.e. (secx)(cosx) = 1

tan^2x = (secx) + 1

and so on, is there any easy way for me to remember them?

Not knowing what the 8 are, I will just say that one way to memorize a collection of related stuff, is to distill it down to as few central facts and principles as possible, and then memorize those:

sinθ is the "height" of θ in the unit circle, i.e., its y-coordinate.
cosθ is the "base" of θ in the unit circle, i.e., its x-coordinate.

And since you already know that the unit circle is given by
x^2 + y^2 = 1,
You can immediately conclude that
(sinθ)^2 + (cosθ)^2 = 1

Then you have to memorize the definitions of the other 4 common trig functions:
tanθ = sinθ/cosθ
cotθ = cosθ/sinθ
secθ = 1/cosθ
cscθ = 1/sinθ

But here's a little trick to condense those somewhat. Just memorize the definition of the tangent:
tanθ = sinθ/cosθ

Then memorize the "regular" order of the 6 trig fns:
sin, cos, tan, cot, sec, csc.

Then "fold" the list in half, back under itself:
sin, cos, tan,
csc, sec, cot

The up-down pairs are now mutually reciprocal, and that's 3 of your identities:
sinθ cscθ = cosθ secθ = tanθ cotθ = 1

Then, as Capt.Matticus points out, you can start with the 1st identity we wrote:
(sinθ)^2 + (cosθ)^2 = 1
and divide both sides by either (sinθ)^2 or (cosθ)^2 to get the 2 identities:
1 + (cotθ)^2 = (cscθ)^2
(tanθ)^2 + 1 = (secθ)^2

So that covers 6 basic trig identities. What are the other 2 you need to memorize?

sin(x) * csc(x) = 1
cos(x) * sec(x) = 1
tan(x) * cot(x) = 1

The pythagorean identities:
sin(x)^2 + cos(x)^2 = 1
tan(x)^2 + 1 = sec(x)^2
cot(x)^2 + 1 = csc(x)^2

(note: you can get the second identity by dividing everything in the first identity by cos(x)^2 and you can get the third identity by dividing everything in the first identity by sin(x)^2, so you really only need to be able to remember the first identity)