Adding waves of the same frequency! If I have v_1 = 3sin t and v_2 = 2cos t...

[Vulcan]

Can someone please clarify?

If I have v₁ = 3sin t and v = 2cos t when adding them (v₁ + v₂) we will have sqrt(A² + B²) sin(t - tan^-1(B/A) = sqrt(13) sin(t-0.588)

is it true to say that if it was v₂ + v₁ we would have sqrt(B² + A²) cos(t - tan^-1(A/B) = sqrt(13) cos(t-0.983)

if it is correct, then I am struggling to get the solution of adding v₁=2sin 3t and v₂= 6cos3t which is given as sqrt40 cos(3t+5.961)

I can't find anywhere that explains when to use sin and when to use cos and how to change between them! It will ask to add the two waves in the form of Asin(t+⍺) sometimes and other times in the form Acos(t+⍺).

As always, any help offered is much appreciated

 

[Deleted member 4993]

Can someone please clarify?

If I have v₁ = 3sin t and v = 2cos t when adding them (v₁ + v₂) we will have sqrt(A² + B²) sin(t - tan^-1(B/A) = sqrt(13) sin(t-0.588)

is it true to say that if it was v₂ + v₁ we would have sqrt(B² + A²) cos(t - tan^-1(A/B) = sqrt(13) cos(t-0.983)

if it is correct, then I am struggling to get the solution of adding v₁=2sin 3t and v₂= 6cos3t which is given as sqrt40 cos(3t+5.961)

I can't find anywhere that explains when to use sin and when to use cos and how to change between them! It will ask to add the two waves in the form of Asin(t+⍺) sometimes and other times in the form Acos(t+⍺).

As always, any help offered is much appreciated

A*cos(t+a)=A*sin(t+b)

where

b = a + π/2

 

[Vulcan]

A*cos(t+a)=A*sin(t+b)

where

b = a + π/2

Thanks, I understand that. It was the way it was explained in the book was a bit scant. Sat down this morning and worked everything out, so I understand it much better now.