To find whether x(t) and y(t) signals are same?

[amaresh92]

Homework Statement

let x(t)=cos(ω1(t+τ1) +δ1) and sin (ω2(t+τ2) +δ2)
determine whether both the signal are same for given data
ω1=∏/3 , ω2=∏/3
τ1=0 , τ1=1
δ1=2∏ , δ1=-∏/3

Homework Equations

The Attempt at a Solution

solution is as given-:
as ω1=ω2,
so
ω1τ1+ δ1=ω2τ2+ δ2+2∏k where k is integer
so x(t)=y(t)

i did not understand how they can conclude like that?

 

[tiny-tim]

hi amaresh92!

i assume you mean …

let x(t)=cos(ω1(t+τ1) +δ1) and sin (ω2(t+τ2) +δ2)
determine whether both the signal are same for given data
ω1=∏/3 , ω2=∏/3
τ1=0 , τ₂=1
δ1=2∏ , δ₂=-∏/3

as ω1=ω2,
so
ω1τ1+ δ1=ω2τ2+ δ2+2∏k where k is integer
so x(t)=y(t)

i did not understand how they can conclude like that?

(try using the X₂ button just above the Reply box )

if they were both cos, that would be correct, but since one is cos and the other is sin, it would have to be

ω₁τ₁+ δ₁=ω₂τ₂+ δ₂+2∏k - ∏/2

 

[rude man]

hi amaresh92!

if they were both cos, that would be correct, but since one is cos and the other is sin, it would have to be

ω₁τ₁+ δ₁=ω₂τ₂+ δ₂+2∏k - ∏/2

Oops.
I agree. Now.