I think you have made a mistake with your question, I think you meant to write 3sinθ+5cosθ. If that`s what you meant then if you expand Rsin(θ+α)=Rsinθcosα +RcosθsinαThen equate coefficients:3sinθ=Rsinθcosα therefore 3=Rcosαand 5cosθ = Rcosθsinα therefore 5= Rsinα dive the last two equations Rsinα / Rcosα =tanα = 5/3square and add you get 9+25 = R squared (since square of sine + square of cos is 1), so R=root of 34

If your original question was correct then 3sinθ+5sinθ = 8sinθso R=8 and α = 0