- #1

SubtleAphex

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I'm trying to figure out the steps required to do the following simplification:

This equation:

b/(a^2+ ω^2 )*(-a*sin(ω*t)+ω*cos(ω*t))

can be simplified to the following:

(b/√(a^2+ ω^2 ))*sin(ω*t+ θ)

θ= tan^(-1) (- ω/a)

I can numerically verify that this is true but I am having trouble figuring out the steps to do this simplification. Any help would be greatly appreciated. See attached .doc file for a cleaner presentation of the equations.

This equation:

b/(a^2+ ω^2 )*(-a*sin(ω*t)+ω*cos(ω*t))

can be simplified to the following:

(b/√(a^2+ ω^2 ))*sin(ω*t+ θ)

θ= tan^(-1) (- ω/a)

I can numerically verify that this is true but I am having trouble figuring out the steps to do this simplification. Any help would be greatly appreciated. See attached .doc file for a cleaner presentation of the equations.