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Writing cotangent in terms of cosinehow?

  1. Feb 1, 2010 #1
    1. The problem statement, all variables and given/known data
    How can I write cos(x) in terms of cot(x)? I tried using the pythagorean identities and fundamental identities but still cannot figure it out.
    The answer must start as the following: cosine(x)=.....



    2. Relevant equations
    All the trig identies. I think it wants me to use the fundamental ones but Im not sure thats possible
    http://www.sosmath.com/trig/Trig5/trig5/trig5.html


    3. The attempt at a solution
    I know that cotangent=cos/sin but I need it to only be in terms of cosine which seems impossible to me because I've tried everything. Also, I do believe it is okay to use cot^2(x) with the pythagorean identities.
     
  2. jcsd
  3. Feb 1, 2010 #2

    Mark44

    Staff: Mentor

    Which do you want to do - write cos(x) in terms of cot(x), or cot(x) in terms of cos(x)? Your title and problem statement are at odds. Assuming it's the latter,
    cot(x) = cos(x)/sin(x), and sin2(x) = 1 - cos2(x), hence sin(x) = +/-sqrt(1 - cos2(x)).
     
  4. Feb 1, 2010 #3
    I want to express cosine in terms of cotangent. Cosine is y and cotangent is x, so I want to express y in terms of x
    sounds confusing which is why I am having trouble with it
     
  5. Feb 1, 2010 #4

    Mark44

    Staff: Mentor

    cos(x) = [cos(x)/sin(x)]*sin(x) = cot(x)*sin(x) = cot(x) * 1/csc(x)

    Now use the identity that cot2(x) = 1 - csc2(x), solving for csc2(x) first, and then csc(x). Use that to replace 1/csc(x) in the formula above. That will give you cos(x) in terms of cot(x).
     
  6. Feb 1, 2010 #5
    i thought 1/csc is equal to sin? and 1/sec= cos. and cosine is what im trying to use.

    maybe i am reading your post wrong...
     
  7. Feb 1, 2010 #6
    oh and i see how you may be confused, the title of the thread is wrong. sorry

    i need cosine in terms of cotangent
     
  8. Feb 1, 2010 #7

    Mentallic

    User Avatar
    Homework Helper

    Yes but Mark is telling you to use an identity that involves csc(x) and cot(x). See if you can complete where he was leading you.
     
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