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Trig Identity Question Sort of

  1. Nov 15, 2009 #1
    1. The problem statement, all variables and given/known data

    Okay so the objective here is to express

    y(t) = cos(t - b) - cos(t)

    in the form

    y(t) = Asin(t - c)

    where A and c are in terms of b.


    2. Relevant equations

    For easy reference, here is a table of identities:
    http://www.sosmath.com/trig/Trig5/trig5/trig5.html

    3. The attempt at a solution

    Well, using the sum and difference formulas, I got that

    y(t) = cost(cosb - 1) + sint*sinb

    equating this to the desired expression gives

    cost(cosb - 1) + sint*sinb = Asin(t - c)
    cost(cosb - 1) + sint*sinb = A(sint)(cosc) - A(cost)(sinc)

    So thus I determined that

    cosb - 1 = -Asinc (1)
    sinb = Acosc (2)

    Squaring both sides and adding gave me, eventually,

    A^2 = -2cosb + 1

    So would A be +/- sqrt(-2cosb + 1) ?

    Then I did almost the exact same thing for c simply by moving the -1 on the left side of (1) to the right:

    cosb = -Asinc + 1 (1*)
    sinb = Acosc (2)

    Squaring and adding I got

    A^2 - 2Asinc = 0

    A - 2sinc = 0

    sinc = A/2

    so then would c = arcsin(A/2)?


    I don't even know if I am doing this right so any assistance would be great!

    Thank you.
     
    Last edited: Nov 15, 2009
  2. jcsd
  3. Nov 15, 2009 #2
    It is very hard to read it but squaring and ading (1) and (2) should give A^2 on the right side but looks like you simplified.

    Yes, you are using the right approach. In case you missed second step is to divide (1) by (2) to get second equation.
    A.tan(c) = ....
     
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