Phasors - Converting from sine to cosine

Discussion in 'Homework Help' started by testing12, Mar 27, 2011.

Jan 30, 2011
80
2
Hello Everyone,

Im having some trouble with phasors.
My objective is to convert expressions such as:
- 8 sin(10t rad+70 degrees) and
120 sin (10t rad -50 degrees)

to an expression with cosine and the positive amplitude. I cannot seem to get them correct! either i add 90 degrees when im supposed to subtract or subtract when adding is required.

Can some one please help me, my text does a very brief job of explaining this, and rightfully so since i should know this already!

Regards.

Jan 30, 2011
80
2
For example here is one where I went wrong, but i just dont understand it. Im using the method from the text book. They say to use the vertical axis as sin (wt) and horizontal axis as cos (wt) but the vertical axis is inverted, that is the top is - and bottom is +.

3. t_n_k AAC Fanatic!

Mar 6, 2009
5,448
789
I would keep two relationships in mind

1. sinθ=cos(90-θ) - for the right angled triangle
2. cos(α)=cos(-α)
So take the case of

v(t)=120sin(10t-50°)

let θ=[10t-50]

v(t)=120cos(90°-[10t-50°])=120cos(90°-10t+50°)

or

v(t)=120cos(140°-10t)

let
α=140°-10t=-(10t-140°)
&
-α=(10t-140°)

so from (2) above
cos(α)=cos(-α)
cos(140°-10t)=cos(10t-140°)

Hence

v(t)=120cos(10t-140°)