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Va = 2 sin (314.2t) + Vb = 2 sin(314.2t - 120°)

Any help would be greatly appreciated.

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- #1

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Va = 2 sin (314.2t) + Vb = 2 sin(314.2t - 120°)

Any help would be greatly appreciated.

- #2

arildno

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Va = 2 sin (314.2t) + Vb = 2 sin(314.2t - 120°)

Not until you correct such sloppiness in writing.

Not until you correct such sloppiness in writing.

- #3

arildno

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Furthermore, do NOT make approx like 100*pi=314.2. I'm sure your book wrote 100*pi??

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This is what really annoys people about forums lots of arsey know-it-alls who don't want to help just to show off how clever they are. Well done you

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arildno

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I have two expressions Va = 2 sin (314.2t) and Vb = 2 sin (314.2t - 120°) and I need to know how to add them together and express the answer in the same form.

I do not know how to do this as I have never been taught so if you would like to help me that would be fantastic however if you would prefer to belittle me some more please feel free.

- #7

arildno

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THAT is how you should write it!

What you WROTE however, "Va = 2 sin (314.2t) + Vb = 2 sin(314.2t - 120°)" means something completely different, namely:

1. Va=2sin(314.2t)+Vb

and

2. 2sin(314.2t)+Vb=2sin(314.2t-120deg)

This means that, for example, combining 1 and 2, Va=2sin(314.2t-120deg)

and using this in 1., you may find Vb=2sin(314.2t-120deg)-2sin(314.2t)

That isn't quite what you meant, was it?

So, it is not about me "being offended", but that you should become aware how CAREFUL you must be not to make sloppinesses (and, believe me, it is sloppiness which comes NATURALLY to all of us, becoming careful needs lots of work!)

Before proceeding, do you see my point now?

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- #9

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##2\sin(314.5t)+2\sin(314.5t-120)##

as a single term? If that is the case, there is an identity that allows you to combine such terms. It is near the bottom of the page here. If that is not what you are looking for, or you are still struggling to find the identity on that page, mention it.

PS this should probably be in "homework help"

- #10

arildno

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If you had Sin(A)+Sin(B), could you make this into a simplified product expression?

- #11

arildno

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Sloppiness occurs naturally, and there is no shame in that; the important thing is not to become of self-defensive if somebody tells you of it, but rather take a step back and think: "Hmm..perhaps I was sloppy? Let me just check one more time.."

In that manner, actual INSTANCES of sloppiness will decrease fast, because you let the ambition to always be most critical to yourself guide your work, acknowledging that in the beginning, others' criticisms might be beneficial spurs to develop the actually very difficult skill of being self-critical of work you have invested a lot of work in.

See if the advices given you of Sin(A)+Sin(B) leads you somewhere, hmm?

- #12

Mark44

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Using "+" to represent "and" was very confusing to the folks responding in this thread. What you wrote says that Va equals 2 sin (314.2t) + Vb, which in turn is equal to 2 sin(314.2t - 120°).

Va = 2 sin (314.2t) + Vb = 2 sin(314.2t - 120°)

Any help would be greatly appreciated.

- #13

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DrewD I am new to this forum and only realised after I posted that it was in the wrong section. I will be more careful in future.

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I have drawn the two sine waves on a graph and created a table of values, I have added these together and plotted the resultant wave. This has confused me even more because when I use any of the equations I have found online to calculate a given point it does not match. This says to me that I have miscalculated my points (which I don't think is the case as I have checked and double checked) or I still haven't found the right information.

If anyone can give me a bit more of a clue I would be most grateful.

- #15

arildno

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Now, simplify the expression Va+Vb=2*(Sin(A)+Sin(B)) using a trigonometric identity.

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This is a very nice bit of graphing practice, but don't do that. If you want, you can use a graphing calculator or online grapher like desmos.com, but I would not waste my time graphing by hand except for data.I have drawn the two sine waves on a graph and created a table of values, I have added these together and plotted the resultant wave.

What information have you found? arildno simplified the problem for you. Which identity would you use?This has confused me even more because when I use any of the equations I have found online to calculate a given point it does not match. This says to me that I have miscalculated my points (which I don't think is the case as I have checked and double checked) or I still haven't found the right information.

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Unfortunately I work full time and have family responsibilities and I don't have any more time to dedicate to this. So I am officially throwing the towel.

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arildno

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[tex]\sin(u)+\sin(v)=2sin(\frac{u+v}{2})\cos(\frac{u-v}{2})[/tex]

use that one, with A=u and B=v.

Afterwards, insert your original expressions for A and B and simplify.

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Thank you for your patience.

- #20

arildno

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Honestly, I do not see what problems you have reached into, and I am actually inclined to believe you have misunderstood the right answer as somehow not being what you were asked for.

- #21

ehild

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You have to write the sum of two sine (cosine) functions of formSo as it stands, your problem is finding how to rewrite

##2\sin(314.5t)+2\sin(314.5t-120)##

as a single term? If that is the case, there is an identity that allows you to combine such terms. It is near the bottom of the page ="http://www.sosmath.com/trig/Trig5/trig5/trig5.html"]here. If that is not what you are looking for, or you are still struggling to find the identity on that page, mention it.

PS this should probably be in "homework help"

sin(a+b)=sin(a) cos(b) + cos(a) sin(b)

(or cos(a+b)=cos(a)cos(b)-sin(a)sin(b))

You get :

V

With those, the equation V

Asin(wt)+B sin(wt)cos(β)+Bcos(wt)sin(β)=Csin(wt)cos(γ)+Ccos(wt)sin(γ).

Collect all the sin(wt) terms and also the cos(wt) terms:

sin(wt)[A+Bcos(β)-Ccos(γ)] + cos(wt)[Bsin(β)-Csin(γ)]= 0

You have to find the unknown C and γ so that the equation holds at any time t.

For t=0, sin(wt)=0 cos(wt)=±1, so

If wt=pi/2 radian (t=pi/(2w) cos(wt)=0 and sin(wt)=±1, so

You have to solve the system of equation in bold.

Bsin(β)=Csin(γ)

A+Bcos(β)=Ccos(γ)

Square both equations and add them together.

(Bsin(β))

You can expand and simplify the left hand side:

Knowing C, sin(γ)=B/C and cos(γ)=(A+Bcos(β))/C.

Apply to your problem: A=B=2, β=-120 degrees. (:Edited)

ehild

Last edited:

- #22

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Vc = 2.0007sin(314.2t-59.99°)

Thank you all for your help and if someone would confirm my answer for my peace of mind that would be great.

- #23

ehild

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(I had an error in my previous post, beta was -120° instead of 120°.)

ehild

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Thank you ehild

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arildno

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