How can I improve my understanding of trigonometry for Calculus II?

[Pythagorean]

I skipped college albebra and trigonometry and went straight into Calculus. It was fairly easy, I had to learn trig as I went, but I got an A.

I'm now in Calc II, using a different book through a different school (A university rather than a campus) and I'm starting to have troubles.

Is there a book or a site or a clever system I can study that will broaden my trig understanding? I've considered just buying a trig textbook from the campus bookstore.

I've studied the unit circle a lot and played with it on my own, and I have friend that has developed an awesome diagram for multiplication and addition of trig functions, but I assume working through problems is the best thing I can do, but these books are so &%*@&$ expen$ive

 

[mathwonk]

the best way is to realize that trig is a special case of the exponential fuinction studied in calculus, and use that to shortcut learning trig.

I myself skipped trig in high school and never learned the usual trig until i had to teach it. the main pooint is that e^(ix) = cos(x) +isin(x), where e^z is defiend by the powers eries e^z = 1 + z + z^2/2! + z^3/3! + z^4/4! +... for any complex number z.


then one defiens cos and sin by soilving the equation abovce.

i.e. cos(x) = (1/2)[e^(ix) + e^(-ix)] and sin(x) = (1/2i)[e^(ix) - e^(-ix)].

Then one proves that e^(x+y) = e^x e^y, and that [e^x]^y = e^[xy].

One deduces that cos(x+y) = cos(x)cos(y) - sin(x)sin(y),

and sin(x+y) = cos(x)sin(y) + cos(y)sin(x). (I hope)


since also e^(2<pi>i) = 1, one concludes that cos and sin are periodic with period 2<pi>.

tyhis reduces the compicated laws for trig functions to the simpler laws for exponential functions and makes life simpler.

 

[modmans2ndcoming]

Calc 2 is tougher than Calc 1, especially in how you apply trig... just wait for integration methods...trig plays a major role.

I took trig in high school and did not take it seriously so when I got to college and got to calc 2 it had been about 3 years since I took my have effort trig class. I basically had to take a crash course in trig and muscle my way through. I found that the amount of trig in Calc 2 was sufficient for me to become good enough at it, and I got better as I went along. Sure, I was lost some times and I had to take a few more minutes to figure something out at first, but by the final, I knew what identities to use and how to use them.

 

[Pythagorean]

yeah, we're on trig substitution right now. I guess just doing the problems and writing down my realizations as notes is the best way to go about it.

The power series is kind of tough to use since I haven't had much practice with it. I have a friend who showed me a bit about that, but it's sometimes just more practical to memorize things.

The ah-ha! moment will come to me sooner or later after I memorize. I guess that's a weird learning style, but it's what I've found works best for me, despite my hate for memorizing vs. learning