#### freckles101

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Express f(t) in the form: Acos(ωt-ϕ)

f(t)=-12 sin(5t+2)-9 cos(5t-8)

f(t)=-12 sin(5t+2)-9 cos(5t-8)

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- Thread starter freckles101
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Express f(t) in the form: Acos(ωt-ϕ)

f(t)=-12 sin(5t+2)-9 cos(5t-8)

f(t)=-12 sin(5t+2)-9 cos(5t-8)

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Expand using the Compound Angle formulae and gather like terms,Express f(t) in the form: Acos(ωt-ϕ)

f(t)=-12 sin(5t+2)-9 cos(5t-8)

Continue....

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That's great adviceExpand using the Compound Angle formulae and gather like terms,

convert to Wave Function.then

Continue....

I'd keep the answer exact by declaring two constants [imath]c_1=-(?\sin(?) + ?\cos(?))\text{ and } c_2=[/imath] something similarNB:[/B] Justyour work is to 2 (or 3) decimal places to permit the use of \(\displaystyle =\text{instead of} \approx \)state

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Whilst mathematically 'sound', I find introducing more 'letters' can cause confusion (they can start toThat's great advice

I'd keep the answer exact by declaring two constants [imath]c_1=-(?\sin(?) + ?\cos(?))\text{ and } c_2=[/imath] something similar

Working to 2/3 d.p. throughout produces a final answer for the phase angle that is (usually) in keeping with what you get

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Glad we were able to help.

Feel free to post your working & answer and we'll let you know if it's right.

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Hi freckles,thank you so much!! please excuse my messy writing! but does this look okay?

I'm afraid that's not what I get.

Let me check through your working and I'll try to explain where you've gone wrong.

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I looked at your working and you started off correctly, by Expanding using the Compound Angle formulae (as I suggested) but then you went completely awry I’m afraid.

Rather than pick through everything you have written, it is easier for me to show you the method I used. I haven’t bothered to check your actual arithmetic (or sign handling) because you diverged from the correct approach right after expanding the initial expression, so here’s one way to get the right answer:-

I would begin by

Starting with:

\(\displaystyle -12sin (5t+2)-9cos(5t-8)\)

You (correctly) expanded this to:\(\displaystyle -12(sin5tcos2+cos5tsin2)-9(cos5tcos8+sin5tsin8)\)

However, after that, you appear to have attempted to “simplify” your new expression into two

When I said “gather like terms” what I meant was to,

Cubist's suggestion of using constants (like c

Thus we can now

\(\displaystyle -12(-0.42sin5t+0.91cos5t)-9(-0.15cos5t+0.99sin5t)\)

And we can now expand the brackets by multiplying by the -12 & the -9 to get:

\(\displaystyle 4.99sin5t-10.91cos5t+1.31cos5t-8.90sin5t\)

\(\displaystyle -9.6cos5t-3.91sin5t\)

ie: a form you

So the complete working should look like this:

\(\displaystyle -12sin (5t+2)-9cos(5t-8)\)

\(\displaystyle =-12(sin5tcos2+cos5tsin2)-9(cos5tcos8+sin5tsin8)\)

\(\displaystyle =-12(-0.42sin5t+0.91cos5t)-9(-0.15cos5t+0.99sin5t)\)

\(\displaystyle =4.99sin5t-10.91cos5t+1.31cos5t-8.90sin5t\)

\(\displaystyle =-9.60cos5t-3.91sin5t\)

I would strongly recommend that

\(\displaystyle A=\sqrt{9.60^2+3.91^2}=10.37\) (Ignoring the minus signs because you are squaring.)

and

\(\displaystyle θ=tan^{-1}\left(\frac{-3.91}{-9.60}\right)=0.39\)

\(\displaystyle \Rightarrow \text{ϕ}=\pi+0.39=3.53\)

\(\displaystyle \Rightarrow -12sin (5t+2)-9cos(5t-8)=10.37cos(5t-3.53)\)

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The "working" you provided also gave me some concerns about how you were calculating the Phase Angle (which is why I said you should do it yourself before looking at my calculation).

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Haha yeah, I rushed through that one, and have noticed a few algebraic mistakes... I've since typed it out with the corrections i saw that were required... does this look closer to the answer you got? Thank you so much for your support and assistance!!Hi freckles,

I'm afraid that's not what I get.

Let me check through your working and I'll try to explain where you've gone wrong.

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No, I’m sorry but that’sHaha yeah, I rushed through that one, and have noticed a few algebraic mistakes... I've since typed it out with the corrections i saw that were required... does this look closer to the answer you got? Thank you so much for your support and assistance!!

View attachment 32753

Now that you have typed it out nice and clearly, with explanations, I can see what you were trying to do and your method (

However, your “terminology” is all wrong and could be construed as showing a lack of understanding of what you are about; have you copied this ‘method’ from somewhere?

For example, you

You could (

Ignoring your persistent (terminological) mistakes that (all) arise from this confusion, your subsequent calculations

Using those numbers you could then have written:

(Doing so can save a lot of time (& confusion) when we are considering your problem(s)!)

which

which is the form that converts (by the 'usual' method) to

Basically, what you are doing is what Cubist suggested and delaying the evaluation of these coefficients right to the end but you are naming everything

Unfortunately, however, just as I suspected, (see my comments above about your calculation of the Phase Angle; at the end of Post #10 and, again, in Post #11), you

Did you read my posts

If you are likely to face this kind of problem again, I would suggest that you have a good read through my post (#10) and compare what I have laid out there with the method you have pursued. IMNSHO, my method is a lot simpler to both follow

Please read, carefully, what I posted previously (#10) and let us know that you understand what is there, how it

Cheers, B.

Last edited:

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You could (

Sheesh! Even more complicated!

(I'm not 'fixing' the bit further down! )