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

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- April 22nd 2011, 09:21 PMpcalhelpf(x)=3sin x+4sin(x-3)
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 - April 22nd 2011, 09:45 PMabhishekkgp
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.