1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Trigonometric manipulation

  1. Nov 1, 2013 #1

    Probably a simple problem, but Im not able to figure it out.

    [tex] a \cos (\epsilon) - b \sin (\epsilon) = c [/tex] in-phase part
    [tex] a \sin (\epsilon) - b \cos (\epsilon) = d [/tex] out-of-phase part

    In order to find the phase shift, the in-phase term has to be divided by the out-of-phase term?

    [tex] \frac{a \cos (\epsilon) - b \sin (\epsilon) = c}{a \sin (\epsilon) - b \cos (\epsilon) = d} [/tex]

    And the phase shift is the arctan of the out of phase and the in-phase term to my knowledge. But I am not able to manipulate the formula in a way that I'll get to an arctan. Can someone point me in the right direction?

  2. jcsd
  3. Nov 1, 2013 #2
    $$ a \cos x + b \sin x = \sqrt {a^2 + b^2 } ( \frac a {\sqrt {a^2 + b^2} } \cos x + b \frac b {\sqrt {a^2 + b^2} } \sin x)
    \\ = \sqrt {a^2 + b^2 } ( \sin c \cos x + \cos c \sin x) = \ ...
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Trigonometric manipulation
  1. Algebraic manipulation (Replies: 2)

  2. Trigonometric equation (Replies: 2)