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Finding the Value of cot(pi/8) in the form a + b*sqrt(2)

  1. Apr 9, 2015 #1
    1. The problem statement, all variables and given/known data
    Show that sin(2θ) / (1 + cos(2θ) = tan(θ) - I've completed this part
    Hence find the value of cot(π/8) in the form a + b√(2), where a, b ∈ ℤ
    2. Relevant equations
    cot(θ) = (1 + cos(2θ)) / sin(2θ)

    3. The attempt at a solution
    I did the math, got (1 + cos(π/4)) / sin(π/4) = (1 + 1/2√(2)) / (1/2√(2)) = (2 + √(2)) / √(2) = (2 / √(2)) + 1
    Assuming I did all the math correctly, I can't figure out how to get to a + b√(2) from here.
    Any tips?

    (Also if anyone can answer this, how can I make my math look more "math-like" in these forums? I hate having to insert math as typed up stuff that looks sloppy)

    Thanks very much for any help anyone can offer!
     
  2. jcsd
  3. Apr 9, 2015 #2

    Dick

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    Science Advisor
    Homework Helper

    Isn't ##\frac{2}{\sqrt{2}}=\sqrt{2}##? I'll try and find a link to a TeX tutorial on the website to help you make your stuff look more "math-like".
     
  4. Apr 9, 2015 #3

    SammyS

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    Staff Emeritus
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    Write ##\displaystyle\ \frac{1+\cos(2\theta)}{\sin(2\theta)}\ ## as ##\displaystyle\ \frac{1}{\sin(2\theta)}+\frac{\cos(2\theta)}{\sin(2\theta)}\ ## .

    (Use LaTeX for math-like stuff.) LaTeX Guide
     
  5. Apr 9, 2015 #4
    your math is correct, you can write it as [itex]1 + \sqrt{2} [/itex]

    a=b=1

    To write math equations write the word "itex" in [], and when you're done write "itex" after the dash in [ /]
    there may be a shortcut to that, though
     
  6. Apr 9, 2015 #5
    Thank you very much for your help! I should've considered rearranging the problem in the first place to get that answer, but I guess I just wasn't thinking of it at the time. It always bug me when I miss one small thing that could lead me to the answer. Also, thanks for introducing me to LaTeX! I'm going to have to look more into that.
     
  7. Apr 10, 2015 #6

    Mark44

    Staff: Mentor

    There is a shortcut that I find easier to type. Instead of itex tags, use a ## pair at the beginning and another pair at the end. Use those for inline math stuff.

    For standalone math stuff use a pair of $$ at the start and another pair at the end. These are equivalent to the [ tex ] and [ /tex ] tags.
     
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