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Question in trigonometry

  1. Jan 4, 2008 #1
    If tan2x=(-24/7), find the exact value(s) of sinx and cosx

    Working out the answers by hand, I get

    sinx = ±3/5, ±4/5
    cosx = ±3/5, ±4/5

    But by actually calculating x and plugging it into sinx and cosx, I get

    sinx = 3/5, 4/5
    cosx = 3/5, -4/5

    I'm pretty sure that the latter are the answers, but how do I justify it given the ±?

    Thanks! :smile:
  2. jcsd
  3. Jan 4, 2008 #2
  4. Jan 4, 2008 #3
    Here's what I did:

    tan2x = -24/7

    so to find cosx and sinx, I established that on a graph:
    y = -24
    x = 7
    r = 25


    y = 24
    x = -7
    r = 25

    Thus, cos2x = ±7/25. By breaking down cos2x into (1-2(sinx)^2) and (2(cosx)^2-1) and working out the answers, I got four values, as listed in my previous post.

    EDIT: Sorry, I meant eight values, counting the ±'s. I'm supposed to get four.
    Last edited: Jan 4, 2008
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