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

Question

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

i might be wrong though, one sec.

anonymous · Answer

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

anonymous · Answer

what joe said

anonymous · Answer