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Behind on Trig Identities

  1. Sep 4, 2011 #1
    I am currently taking Calc II and we are doing trig substitutions at the moment. I seem to have forgotten almost all the important trig identities. I understand that this sounds like something I should google but I honestly cannot find a good list of the trig identities I should know at this point. If someone could help me with the trig identities that I should memorize I would appreciate it. Thank you.

    Edit: An example would be sin(2x)=2sin(x)cos(x) or tan2(x)=sec2(x)-1. Those are two I remember but I know I am forgetting a ton.
     
    Last edited: Sep 4, 2011
  2. jcsd
  3. Sep 4, 2011 #2

    rock.freak667

    User Avatar
    Homework Helper

    http://www.sosmath.com/trig/Trig5/trig5/trig5.html" [Broken]

    Try to learn them when doing questions or else you'll be trying to learn a long list where you may struggle to see when to use it in a given question.
     
    Last edited by a moderator: May 5, 2017
  4. Sep 4, 2011 #3
    Thank you, that really helped.
     
    Last edited by a moderator: May 5, 2017
  5. Sep 4, 2011 #4
    I made flashcards, but I agree that you need to practice them with problems. Here are a few of mine:

    [itex]
    \sin ^2 x + \cos ^2 x = 1
    [/itex]

    [itex]
    1 - \sin ^2 x = \cos ^2 x
    [/itex]

    [itex]
    1 - \cos ^2 x = \sin ^2 x
    [/itex]

    [itex]
    \sec ^2 x - \tan ^2 x = 1
    [/itex]

    [itex]
    \sec ^2 x - 1 = \tan ^2 x
    [/itex]

    [itex]
    \sec ^2 x = 1 + \tan ^2 x
    [/itex]

    [itex]
    \csc ^2 x - \cot ^2 x = 1
    [/itex]

    [itex]
    1 + \cot ^2 x = \csc ^2 x
    [/itex]

    [itex]
    \csc ^2 x - 1 = \cot ^2 x
    [/itex]


    I don't often run into the half angle identities, but they come up occasionally.
     
    Last edited: Sep 4, 2011
  6. Sep 4, 2011 #5

    gb7nash

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    Homework Helper

    Here's a little trick, so that you don't need to rely on brute memorization. We want to memorize the following well-known identity:

    [tex]sin^2 x + cos^2 x = 1[/tex]

    If you divide both sides by cos2x, you get:

    [tex]tan^2 x + 1 = sec^2 x[/tex]

    which is the second identity rearranged. Similarly, if you divide both sides by sin2x, you get:

    [tex]1+cot^2 x = csc^2 x[/tex]

    which is the third identity rearranged. I can't think of any other identities that can be derived like this, but this saves the effort of memorizing, or provides a sanity check to make sure that what you memorized is correct.
     
  7. Sep 4, 2011 #6
    Agreed, my method was the memorize the big three and manipulate them.
     
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