Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Calc II Suggestions

  1. Sep 16, 2004 #1

    Pythagorean

    User Avatar
    Gold Member

    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 text book 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
     
  2. jcsd
  3. Sep 16, 2004 #2

    mathwonk

    User Avatar
    Science Advisor
    Homework Helper

    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.
     
  4. Sep 17, 2004 #3
    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.
     
  5. Sep 17, 2004 #4

    Pythagorean

    User Avatar
    Gold Member

    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 wierd learning style, but it's what I've found works best for me, despite my hate for memorizing vs. learning
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook