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February 23rd, 2013, 01:05 AM   #1
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So confused with this

Heres the Q:

Two signals are received at a satellite tracking station. They are modelled mathematically by the functions:
f(t) = 10cos(16t + pi)
g(t) = 10cos (20t - pi)

The signals are added together, i.e. the function h(t) = f(t) + g(t) is formed.

(a) Use trigonometric formulae to obtain the function h(t).

(b) Obtain a graph of the function h(t).

(c) Find an expression for dh/dt using the product rule and showing all workings out


Now i know what a cosine wave looks like, but i really have no idea how to do this??
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February 23rd, 2013, 01:18 AM   #2
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Re: So confused with this

Since you are instructed to differentiate using the product rule, you need to use the sum-to-product identity:



Then you could use:



Can you proceed?
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February 23rd, 2013, 02:36 AM   #3
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Re: So confused with this

Ive never seen that equation. Oh dear
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February 23rd, 2013, 02:41 AM   #4
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Re: So confused with this

Can you apply it?
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February 23rd, 2013, 02:58 AM   #5
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Re: So confused with this

Ive tried to have a go, but im really confusing myself
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February 23rd, 2013, 10:01 AM   #6
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Re: So confused with this

I would begin with:



Now, applying the sum-to-product identity, we have:





Now using the identities and we have:



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