Question

How to rewrite r Cos(a t)+ s Sin(at) into single sinusoidal ? @M How to rewrite r Cos(a t)+ s Sin(at) into single sinusoidal ? @M @Mathematics

Answer 1

hm i think i know it without the "a" part because i just looked this up the other week

Answer 2

i believe its:\[A\sin(at+\phi)\]where \[A=\sqrt{r^2+s^2},\phi=\tan^{-1}\frac{s}{r}\]

Answer 3

i might be wrong though, one sec.

Answer 4

write it as
\[\sqrt{r^2+s^2}\cos(t-\theta)\] where
\[\tan(\theta)=\frac{s}{r}\]

Answer 5

what joe said

Answer 6

here is a reasonable explanation, but i saw a better one in a wiki that i cannot seem to find again
http://www.mathcentre.ac.uk/resources/workbooks/mathcentre/web-rcostheta-alphaetc.pdf