- #1
fonz
- 151
- 5
Homework Statement
Express 3sin(ωt) + 2cos(ωt) in the form Rsin(ωt + α)
AND
verify the resultant function is the same frequency as 3sin(ωt) and 2cos(ωt)
Homework Equations
R = √a2+b2
α = arctan(b/a)
The Attempt at a Solution
My attempt using the equations above produces the answer R = √13 and α = 0.6 rad or 33.7°
My argument for the solution being the same frequency is that the period T = 2∏/ω in each case therefore f = 1/T = ω/2∏
I have my doubts about this solution because I believe the marks are awarded for a solution involving the double and compound angle formula (I can't see how this is necessary).
Also, is the statement regarding frequency comprehensive enough or is there a better way of presenting the solution?