# Analysing Graphical and Analytical Methods

#### jayb123

##### New member
Good morning all,

I'm doing some course work for an HNC and have got a bit stuck on a question and hope somebody could be of some assistance;

"Two signals are are sensed by a signal processor

V1=40sin(4t)
V2=Acos(4t)

The signal processor adds the signal together to form a third signal that can be described as;

50sin(4t+α)

Determine the value of A (the amplitude of 𝑣 2 ).

Use to plot/model the inputs and output of the signal processor. How do you think graphical methods of sine wave combination compare with analytical methods?"

By using the Sin(a+b) and some basic trig I've come up with A=30 and α=(36.87deg=0.644rad)

I have then graphed the signals as F(x)=40sin(x) etc.

The issue I'm having is explaining how the graphical methods of sine wave combination compare with analytical methods. If any of you can shed some light and help me understand further it would be appreciated massively.

I'll attach an image of the three waves I've got to below.

Many Thanks

Graphs

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To reiterate;

Anyone?

#### Dr.Peterson

##### Elite Member
I'm just not sure what the question means by "graphical methods"; and you haven't shown your actual work for the "analytical method", which I assume means applying identities to rewrite $$\displaystyle 40 \cos(4t) + A \cos(4t)$$ as $$\displaystyle B \sin(4t + \alpha)$$ as you appear to have done.

Have you been taught some specific "graphical methods" for solving this sort of problem? One possibility (rather than just using technology to graph various sums, as you appear to be doing) is along the lines of phasors.

#### HappyScout

##### New member
I'm struggling with a similar problem. But I'm stuck at the 'simple trig'. Can you rearrange trig identities the same as with algebra to solve for A?

#### Dr.Peterson

##### Elite Member
Please submit your request as a new thread, and state clearly what you need to do and what you have tried. We want to see what you have learned, so we can help you use that.

I don't see any "simple trig" here! But what it amounts to is arranging the expression you are given to match the angle-sum identity, as I said in post #5; and that can be turned into a routine method if you need to do it regularly. I'm pretty sure you can find explanations of it on here, or we can give you one.