# Math Help - f(x)=3sin x+4sin(x-3)

1. ## f(x)=3sin x+4sin(x-3)

1) If f(x)=3sin x+4sin(x-3) what is the amplitude and period (p) of f(x)?
A) a= 1.114, p = 6.283
B) a= 1.114, p = 3.141
C) a =2.28, p= 3.141
D) a=7, p = 6.283
E) a= 7, p= 9.425

2. Originally Posted by pcalhelp
I got a bunch of homework. But these are the hardest. Others I could have some clues to solve, but for these I'm clueless. Please help

1) If f(x)=3sin x+4sin(x-3) what is the amplitude and period (p) of f(x)?
A) a= 1.114, p = 6.283
B) a= 1.114, p = 3.141
C) a =2.28, p= 3.141
D) a=7, p = 6.283
E) a= 7, p= 9.425
use sin(x-3)= sin(x)cos(3)-cos(x)sin(3).
then f(x) takes the form p(sinx) + q(cosx).
its maximum value is sqrt(p^2+q^2).

to see this let sqrt(p^2+q^2)=k
then f(x)=p(sinx)+q(cosx)= k[(p/k)(sinx)+ (q/k)(cosx)].
observe that p/k can be taken as cos of some angle say 'y' so p/k=cosy.
this forces q/k=siny.

f(x)= k[(cosy)(sinx)+(siny)(cosx)]= k(sin(x+y)). clearly its maximum is k.