Apologies for my other threads. My browser had a weird hiccup and now somehow there are many that are empty. Please delete the others! Sorry! 1. The problem statement, all variables and given/known data I need to express the real part of e^(-t)*sin(3t + ∏) in the form e^(αt)*A*cos(ωt + θ) where A, α, ω and θ are all real numbers. 2. Relevant equations See above. Also, Euler's Formula: e^jθ = cosθ + jsinθ 3. The attempt at a solution My efforts so far have given me the following: Use Euler's Formula to convert: (cos(-t) + jsin(-t))*(sin(3t + ∏) (cos(t) - jsin(t))*(sin(3t + ∏)) cos(t)sin(3t + ∏) + jsin(t)*sin(3t + ∏) Since the later part of the sum is imaginary... cos(t)sin(3t + ∏) Now, I have two questions: 1) Have I erred in using Euler's formula with no complex number j in the exponent initially? 2) What more is there to be done? I thought about initially trying to re-express in a single step knowing that sinx = cos(x - pi/2), but graphing the two did not seem to yield identical results. Any help would be greatly appreciated!